{"id":20,"date":"2023-09-17T11:08:12","date_gmt":"2023-09-17T11:08:12","guid":{"rendered":"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/"},"modified":"2023-09-17T11:08:12","modified_gmt":"2023-09-17T11:08:12","slug":"tipos-de-indeterminacoes-limites-indeterminados","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/","title":{"rendered":"Tipos de indetermina\u00e7\u00f5es (limites indeterminados)"},"content":{"rendered":"<p>Neste artigo explicamos o que \u00e9 indetermina\u00e7\u00e3o. Voc\u00ea descobrir\u00e1 o que s\u00e3o todos os tipos de indetermina\u00e7\u00f5es e como resolv\u00ea-las. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exerc\u00edcios resolvidos passo a passo sobre os limites de fun\u00e7\u00e3o de todas as indetermina\u00e7\u00f5es. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-las-indeterminaciones\"><\/span> O que s\u00e3o indetermina\u00e7\u00f5es?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Indetermina\u00e7\u00f5es, tamb\u00e9m chamadas de formas indeterminadas, s\u00e3o express\u00f5es matem\u00e1ticas que aparecem no c\u00e1lculo dos limites de fun\u00e7\u00f5es cujo resultado n\u00e3o est\u00e1 definido.<\/strong> Assim, para resolver as indetermina\u00e7\u00f5es dos limites, \u00e9 necess\u00e1rio aplicar um procedimento preliminar que depende do tipo de fun\u00e7\u00e3o.<\/p>\n<p> Ou seja, quando obtemos a indetermina\u00e7\u00e3o, n\u00e3o significa que o limite n\u00e3o exista ou que n\u00e3o possa ser resolvido, mas sim que teremos que fazer altera\u00e7\u00f5es na fun\u00e7\u00e3o para encontrar a solu\u00e7\u00e3o do limite. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-indeterminaciones\"><\/span> Tipos de indetermina\u00e7\u00f5es<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> As indetermina\u00e7\u00f5es, ou formas indeterminadas, s\u00e3o classificadas nos seguintes tipos:<\/p>\n<ul>\n<li> <strong>Indetermina\u00e7\u00e3o infinito menos infinito<\/strong> (\u221e-\u221e)<\/li>\n<li> <strong>N\u00famero de indetermina\u00e7\u00e3o entre zero<\/strong> (k\/\u221e)<\/li>\n<li> <strong>Indetermina\u00e7\u00e3o zero entre zero<\/strong> (0\/0)<\/li>\n<li> <strong>Indetermina\u00e7\u00e3o infinita entre o infinito<\/strong> (\u221e\/\u221e)<\/li>\n<li> <strong>Indetermina\u00e7\u00e3o 1 elevada ao infinito<\/strong> (1 <sup>\u221e<\/sup> )<\/li>\n<li> <strong>Indetermina\u00e7\u00e3o zero elevada a zero<\/strong> (0 <sup>0<\/sup> )<\/li>\n<li> <strong style=\"font-family: -apple-system, BlinkMacSystemFont, &quot;Segoe UI&quot;, Roboto, Oxygen-Sans, Ubuntu, Cantarell, &quot;Helvetica Neue&quot;, sans-serif; font-size: 1rem;\">Indetermina\u00e7\u00e3o zero para o infinito<\/strong> <span style=\"font-family: -apple-system, BlinkMacSystemFont, &quot;Segoe UI&quot;, Roboto, Oxygen-Sans, Ubuntu, Cantarell, &quot;Helvetica Neue&quot;, sans-serif; font-size: 1rem; font-weight: inherit;\">(0\u00b7\u221e)<\/span><\/li>\n<li> <strong>Indetermina\u00e7\u00e3o zero elevada ao infinito<\/strong> (0 <sup>\u221e<\/sup> )<\/li>\n<li> <strong>Indetermina\u00e7\u00e3o infinita levada a zero<\/strong> (\u221e <sup>0<\/sup> )<\/li>\n<\/ul>\n<p> Veremos ent\u00e3o como resolver todos os tipos de indetermina\u00e7\u00f5es. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-menos-infinito\"><\/span> Infinito menos indetermina\u00e7\u00e3o infinita<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A <strong>forma indeterminada infinito menos infinito<\/strong> n\u00e3o \u00e9 igual a zero, pois subtra\u00edmos dois n\u00fameros muito grandes mas n\u00e3o sabemos qual \u00e9 maior. O resultado da diferen\u00e7a dos infinitos depende, portanto, da ordem de cada infinito.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-03349653243a9ad62377c721fea0e797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\infty-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Resolver este tipo de indetermina\u00e7\u00e3o n\u00e3o \u00e9 f\u00e1cil, pois dependendo do tipo de fun\u00e7\u00e3o, um procedimento ou outro deve ser aplicado. Portanto, recomendamos que voc\u00ea visualize a explica\u00e7\u00e3o completa no seguinte link:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/indeterminacao-infinito-menos-infinito-%e2%88%9e-%e2%88%9e\/\">como resolver a indetermina\u00e7\u00e3o infinito menos infinito<\/a><\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-numero-entre-cero\"><\/span> N\u00famero de indetermina\u00e7\u00e3o entre zero<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A <strong>indetermina\u00e7\u00e3o de uma constante dividida por zero<\/strong> \u00e9 obtida quando o denominador de uma fun\u00e7\u00e3o racional \u00e9 cancelado.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8d550f72be2a531eb89d5cf200f54dc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{k}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"10\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> O resultado deste tipo de forma indeterminada ser\u00e1 sempre mais infinito, menos infinito ou o limite da fun\u00e7\u00e3o n\u00e3o existir\u00e1. Vejamos como essa indetermina\u00e7\u00e3o \u00e9 calculada resolvendo um limite como exemplo:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f20a823489187682e3becf93cbd93c7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\cfrac{-4}{x^2}=\\cfrac{-4}{0^2}=\\cfrac{-4}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"217\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Obtivemos a indetermina\u00e7\u00e3o de um n\u00famero dividido por zero, <u style=\"text-decoration-color:#FF9B28;\">ent\u00e3o precisamos calcular os limites laterais da fun\u00e7\u00e3o:<\/u><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-84821ecfa11641959a1463c3f2dd00e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0^-}\\cfrac{-4}{0^2}=\\cfrac{-4}{(-0,001)^2}=\\cfrac{-4}{+0}=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"289\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-904f4d1bb401493cdb76cbb9ce607f0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0^+}\\cfrac{-4}{0^2}=\\cfrac{-4}{0,001^2}=\\cfrac{-4}{+0}=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"261\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/limites-laterais\/\">o que s\u00e3o limites laterais?<\/a><\/span><\/p>\n<p> Os dois limites laterais da fun\u00e7\u00e3o d\u00e3o o mesmo resultado, ent\u00e3o por defini\u00e7\u00e3o o limite da fun\u00e7\u00e3o quando x tende a 0 d\u00e1 menos infinito:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c1b718f44360fe4322ba69ee40c9613_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0^-}f(x)=\\lim_{x\\to 0^+}f(x)=-\\infty \\ \\longrightarrow \\ \\lim_{x\\to 0}f(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"401\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Observe que se os limites laterais tivessem dado valores diferentes, o limite da fun\u00e7\u00e3o neste ponto n\u00e3o existiria. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-cero-entre-cero\"><\/span> Zero entre zero indetermina\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> O <strong>limite indeterminado zero dividido por zero<\/strong> \u00e9 muito comum e \u00e9 obtido em fun\u00e7\u00f5es com fra\u00e7\u00f5es em que o numerador e o denominador se cancelam.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f88512bac0562399d5d8e65829073b54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"9\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Este tipo de limite indeterminado \u00e9 resolvido de forma diferente dependendo da fun\u00e7\u00e3o. Por exemplo, se a fun\u00e7\u00e3o tiver ra\u00edzes, diferentes etapas dever\u00e3o ser executadas. Voc\u00ea pode ver as diferentes resolu\u00e7\u00f5es deste tipo de indetermina\u00e7\u00e3o no seguinte link:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/zero-entre-zero-0-0-indeterminacao\/\">como resolver a indetermina\u00e7\u00e3o do zero entre zero<\/a><\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-entre-infinito\"><\/span> Indetermina\u00e7\u00e3o infinita entre o infinito<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>A indetermina\u00e7\u00e3o infinita entre o infinito<\/strong> geralmente ocorre nos limites infinitos de fun\u00e7\u00f5es com fra\u00e7\u00f5es. Embora a indetermina\u00e7\u00e3o seja o quociente de dois infinitos, o resultado n\u00e3o precisa necessariamente ser infinito.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5322af410095265a81aa545e533ebd1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\infty}{\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"18\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Este tipo de forma indeterminada \u00e9 resolvida por compara\u00e7\u00e3o. Ou seja, observa-se o grau do numerador e o grau do denominador e, dependendo de qual for maior, o resultado limite \u00e9 um ou outro. Voc\u00ea pode ver todos os casos no seguinte link:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\">exerc\u00edcios resolvidos sobre limites infinitos entre o infinito<\/a><\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-1-elevado-a-infinito\"><\/span> Indetermina\u00e7\u00e3o 1 elevada ao infinito<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Matematicamente, pode-se pensar que <strong>1 ao infinito<\/strong> d\u00e1 1, j\u00e1 que qualquer pot\u00eancia de 1 \u00e9 igual a 1. Contudo, este termo \u00e9 uma indetermina\u00e7\u00e3o e, portanto, n\u00e3o se pode deduzir o seu resultado t\u00e3o facilmente.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f68a3b617b5f1db37a9beea43e15264f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1^{\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Este tipo de indetermina\u00e7\u00e3o \u00e9 calculado aplicando a seguinte f\u00f3rmula:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e6bc13731241df168c3dc37d3e3b8e58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to+\\infty}f(x)^{g(x)}=\\lim_{x\\to+\\infty}e^{g(x)\\cdot [f(x)-1]}\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"271\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Por exemplo, o seguinte limite \u00e9 indeterminado porque d\u00e1 a pot\u00eancia do infinito:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-96004b3ff4fd888f2e7fbc30a14abf13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to+\\infty}\\left(1-\\frac{1}{x}\\right)^x=\\left(1-\\frac{1}{+\\infty}\\right)^{+\\infty}=(1-0)^{+\\infty}=1^{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"428\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Devemos, portanto, utilizar a f\u00f3rmula para este tipo de indetermina\u00e7\u00e3o:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e577daa5f0e768ca16bfe27a4d7a8a85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to+\\infty}e^{x\\cdot\\left[1-\\frac{1}{x}-1\\right]}=\\lim_{x\\to+\\infty}e^{x\\cdot\\left[-\\frac{1}{x}\\right]}=\\lim_{x\\to+\\infty}e^{-1}=\\frac{1}{e}\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"383\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> E assim j\u00e1 resolvemos o limite indeterminado elevado ao infinito. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-cero-elevado-a-cero\"><\/span> Indetermina\u00e7\u00e3o zero trazida a zero<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>A indetermina\u00e7\u00e3o zero elevada \u00e0 pot\u00eancia zero<\/strong> aparece dentro dos limites de fun\u00e7\u00f5es complicadas.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dfc1e32d3dc765b27701a8576e765fc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0^0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Para resolver esse tipo de limite indeterminado, voc\u00ea deve usar a seguinte propriedade de limite:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-56b621d520e28cf2dbcd93bcd5d35eb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to a}f(x)^{g(x)}=e^{^{\\displaystyle\\lim_{x\\to a}g(x)\\cdot \\ln\\bigl(f(x)\\bigr)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"266\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Por exemplo, o limite a seguir d\u00e1 a forma indeterminada 0 elevado \u00e0 pot\u00eancia de 0:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8680b80b19cae955169d2c0a8ad41f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}\\left(\\frac{1}{x}\\right)^{\\frac{1}{x}}=\\left(\\frac{1}{+\\infty}\\right)^{\\frac{1}{+\\infty}}=0^0\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"251\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Mas se aplicarmos logaritmos ao limite, podemos encontrar o seu valor: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-04165b15f4b40bbe84ae5a4b214d4846_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to +\\infty}\\left(\\frac{1}{x}\\right)^{\\frac{1}{x}}=e^{^{\\displaystyle\\lim_{x\\to +\\infty}\\frac{1}{x}\\cdot \\ln\\left(\\frac{1}{x}\\right)}}=\\\\[5ex]\\displaystyle =e^{^{\\displaystyle\\lim_{x\\to +\\infty}\\frac{\\ln\\left(\\frac{1}{x}\\right)}{x}}}=e^{^{\\displaystyle\\lim_{x\\to +\\infty}\\frac{\\ln1-\\ln x}{x}}}=\\\\[5ex]=\\displaystyle e^{^{\\displaystyle\\lim_{x\\to +\\infty}\\frac{-\\ln x}{x}}}=e^{^{\\displaystyle\\frac{-\\infty}{+\\infty}}}=e^0=1\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"239\" width=\"307\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-cero-por-infinito\"><\/span> Indetermina\u00e7\u00e3o zero para o infinito<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u00c9 dif\u00edcil encontrar a <strong>indetermina\u00e7\u00e3o do produto de zero e infinito<\/strong> , mas isso n\u00e3o significa que seja f\u00e1cil de determinar.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-74b7fdba8e0feae988551f83341ec063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0\\cdot \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> N\u00e3o existe um m\u00e9todo \u00fanico para resolver este tipo de indetermina\u00e7\u00e3o, mas depende do tipo de fun\u00e7\u00e3o. Neste caso, devemos transformar a fun\u00e7\u00e3o em indetermina\u00e7\u00e3o infinita dividida por infinito ou indetermina\u00e7\u00e3o zero dividida por zero, e a partir da\u00ed aplicar os m\u00e9todos de solu\u00e7\u00e3o que vimos acima para cada indetermina\u00e7\u00e3o.<\/p>\n<p> Portanto, se o limite de uma fun\u00e7\u00e3o for 0 e o limite da outra fun\u00e7\u00e3o for \u221e:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ac028c501a7835fdfa3bab5c769849b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to a}f(x)=0\\qquad\\lim_{x\\to a}g(x)=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"243\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Podemos transformar esse tipo indefinidamente fazendo as seguintes altera\u00e7\u00f5es:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df402461269ae26c30768fc0bf83f2ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to a}f(x)\\cdot g(x)\\begin{cases}\\displaystyle\\lim_{x\\to a}\\frac{f(x)}{\\displaystyle\\frac{1}{g(x)}}=\\frac{0}{0}\\\\[10ex]\\displaystyle\\lim_{x\\to a}\\frac{g(x)}{\\displaystyle\\frac{1}{f(x)}}=\\frac{\\infty}{\\infty}\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"174\" width=\"248\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Vamos ver como fazer isso resolvendo um limite indeterminado como exemplo:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-929e74562ababa44a253522d4474afad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty}e^{-x}\\cdot x=e^{-\\infty}\\cdot (+\\infty)=0\\cdot \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"277\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Operamos na fun\u00e7\u00e3o para obter indetermina\u00e7\u00e3o infinita sobre o infinito e ent\u00e3o encontramos o limite: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3c29bbb439514449cd12fd8d66e327af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to +\\infty}e^{-x}\\cdot x=\\lim_{x\\to +\\infty}\\frac{x}{\\displaystyle\\frac{1}{e^{-x}}}=\\\\[6ex]=\\displaystyle \\lim_{x\\to +\\infty}\\frac{x}{e^x}=\\frac{+\\infty}{e^{+\\infty}}=\\frac{+\\infty}{+\\infty}=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"241\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-cero-elevado-a-infinito\"><\/span> Indetermina\u00e7\u00e3o zero elevada ao infinito<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A <strong>indetermina\u00e7\u00e3o zero elevada ao infinito<\/strong> \u00e9 um pouco dif\u00edcil de entender, pois estamos elevando um n\u00famero muito pequeno a um n\u00famero muito grande.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4894b918853d6dca8db65a026b1a349b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0^{\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Quando essas formas indeterminadas s\u00e3o obtidas, deve-se utilizar a seguinte f\u00f3rmula:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-56b621d520e28cf2dbcd93bcd5d35eb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to a}f(x)^{g(x)}=e^{^{\\displaystyle\\lim_{x\\to a}g(x)\\cdot \\ln\\bigl(f(x)\\bigr)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"266\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Vamos resolver um exemplo para entender melhor como calcular esse tipo de indetermina\u00e7\u00e3o: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ca354428ea8889a956a9b77b04a088f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to 0^+}x^{\\frac{1}{x}}=e^{^{\\displaystyle\\lim_{x\\to 0^+}\\frac{1}{x}\\cdot \\ln(x)}}=\\\\[3.5ex]\\displaystyle =e^{^{\\displaystyle\\frac{1}{0^+}\\cdot \\ln(0^+)}}=e^{+\\infty\\cdot (-\\infty)}\\\\[3ex]\\displaystyle =e^{-\\infty}=\\frac{1}{e^{+\\infty}}=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"190\" width=\"221\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-infinito-elevado-a-cero\"><\/span> Indetermina\u00e7\u00e3o infinita levada a zero<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Normalmente, qualquer pot\u00eancia elevada a zero d\u00e1 1, por\u00e9m, a <strong>indetermina\u00e7\u00e3o do infinito elevada a zero<\/strong> n\u00e3o precisa necessariamente ser assim.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a2ef9259a35e0e2f7a176bcdb934ad9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\infty^0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"25\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Assim como nas indetermina\u00e7\u00f5es zero elevado a zero e zero elevado ao infinito, para resolver este tipo de limite indeterminado \u00e9 necess\u00e1rio aplicar logaritmos:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-56b621d520e28cf2dbcd93bcd5d35eb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to a}f(x)^{g(x)}=e^{^{\\displaystyle\\lim_{x\\to a}g(x)\\cdot \\ln\\bigl(f(x)\\bigr)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"266\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Vamos ver como esse tipo de limites indeterminados \u00e9 resolvido calculando um exemplo passo a passo:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a45090015a206189aca3884f8b2cab30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to +\\infty}x^{\\frac{1}{x}}=e^{^{\\displaystyle\\lim_{x\\to +\\infty}\\frac{1}{x}\\cdot \\ln(x)}}=\\\\[3ex]\\displaystyle =e^{^{\\displaystyle\\lim_{x\\to +\\infty}\\frac{\\ln(x)}{x}}}=e^{^{\\displaystyle\\frac{\\ln(+\\infty)}{+\\infty}}}=\\\\[3ex]\\displaystyle =e^{^{\\displaystyle\\frac{+\\infty}{+\\infty}}}=e^0=1\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"199\" width=\"236\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Neste artigo explicamos o que \u00e9 indetermina\u00e7\u00e3o. Voc\u00ea descobrir\u00e1 o que s\u00e3o todos os tipos de indetermina\u00e7\u00f5es e como resolv\u00ea-las. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exerc\u00edcios resolvidos passo a passo sobre os limites de fun\u00e7\u00e3o de todas as indetermina\u00e7\u00f5es. O que s\u00e3o indetermina\u00e7\u00f5es? Indetermina\u00e7\u00f5es, tamb\u00e9m chamadas de formas indeterminadas, s\u00e3o express\u00f5es matem\u00e1ticas que aparecem no &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/\"> <span class=\"screen-reader-text\">Tipos de indetermina\u00e7\u00f5es (limites indeterminados)<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[16],"tags":[],"class_list":["post-20","post","type-post","status-publish","format-standard","hentry","category-limites-de-funcao"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Como resolver todos os tipos de indetermina\u00e7\u00f5es (limites)<\/title>\n<meta name=\"description\" content=\"Como resolver todos os tipos de indetermina\u00e7\u00e3o. \u2705Com exerc\u00edcios resolvidos sobre os limites das fun\u00e7\u00f5es de todas as indetermina\u00e7\u00f5es. \u2705\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Como resolver todos os tipos de indetermina\u00e7\u00f5es (limites)\" \/>\n<meta property=\"og:description\" content=\"Como resolver todos os tipos de indetermina\u00e7\u00e3o. \u2705Com exerc\u00edcios resolvidos sobre os limites das fun\u00e7\u00f5es de todas as indetermina\u00e7\u00f5es. \u2705\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T11:08:12+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-03349653243a9ad62377c721fea0e797_l3.png\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Tipos de indetermina\u00e7\u00f5es (limites indeterminados)\",\"datePublished\":\"2023-09-17T11:08:12+00:00\",\"dateModified\":\"2023-09-17T11:08:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/\"},\"wordCount\":1056,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Limites de fun\u00e7\u00e3o\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/\",\"url\":\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/\",\"name\":\"\u25b7 Como resolver todos os tipos de indetermina\u00e7\u00f5es (limites)\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/#website\"},\"datePublished\":\"2023-09-17T11:08:12+00:00\",\"dateModified\":\"2023-09-17T11:08:12+00:00\",\"description\":\"Como resolver todos os tipos de indetermina\u00e7\u00e3o. \u2705Com exerc\u00edcios resolvidos sobre os limites das fun\u00e7\u00f5es de todas as indetermina\u00e7\u00f5es. \u2705\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Tipos de indetermina\u00e7\u00f5es (limites indeterminados)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/pt\/#website\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"name\":\"Mathority\",\"description\":\"Onde a curiosidade encontra o c\u00e1lculo!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/pt\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\",\"name\":\"Equipe Mathoridade\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Equipe Mathoridade\"},\"sameAs\":[\"http:\/\/mathority.org\/pt\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u25b7 Como resolver todos os tipos de indetermina\u00e7\u00f5es (limites)","description":"Como resolver todos os tipos de indetermina\u00e7\u00e3o. \u2705Com exerc\u00edcios resolvidos sobre os limites das fun\u00e7\u00f5es de todas as indetermina\u00e7\u00f5es. \u2705","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/","og_locale":"pt_BR","og_type":"article","og_title":"\u25b7 Como resolver todos os tipos de indetermina\u00e7\u00f5es (limites)","og_description":"Como resolver todos os tipos de indetermina\u00e7\u00e3o. \u2705Com exerc\u00edcios resolvidos sobre os limites das fun\u00e7\u00f5es de todas as indetermina\u00e7\u00f5es. \u2705","og_url":"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/","article_published_time":"2023-09-17T11:08:12+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-03349653243a9ad62377c721fea0e797_l3.png"}],"author":"Equipe Mathoridade","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Equipe Mathoridade","Est. tempo de leitura":"5 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/"},"author":{"name":"Equipe Mathoridade","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00"},"headline":"Tipos de indetermina\u00e7\u00f5es (limites indeterminados)","datePublished":"2023-09-17T11:08:12+00:00","dateModified":"2023-09-17T11:08:12+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/"},"wordCount":1056,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"articleSection":["Limites de fun\u00e7\u00e3o"],"inLanguage":"pt-BR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/","url":"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/","name":"\u25b7 Como resolver todos os tipos de indetermina\u00e7\u00f5es (limites)","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/#website"},"datePublished":"2023-09-17T11:08:12+00:00","dateModified":"2023-09-17T11:08:12+00:00","description":"Como resolver todos os tipos de indetermina\u00e7\u00e3o. \u2705Com exerc\u00edcios resolvidos sobre os limites das fun\u00e7\u00f5es de todas as indetermina\u00e7\u00f5es. \u2705","breadcrumb":{"@id":"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/pt\/tipos-de-indeterminacoes-limites-indeterminados\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/pt\/"},{"@type":"ListItem","position":2,"name":"Tipos de indetermina\u00e7\u00f5es (limites indeterminados)"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/pt\/#website","url":"https:\/\/mathority.org\/pt\/","name":"Mathority","description":"Onde a curiosidade encontra o c\u00e1lculo!","publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/pt\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"pt-BR"},{"@type":"Organization","@id":"https:\/\/mathority.org\/pt\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/pt\/","logo":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00","name":"Equipe Mathoridade","image":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Equipe Mathoridade"},"sameAs":["http:\/\/mathority.org\/pt"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/20","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/comments?post=20"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/20\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/media?parent=20"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/categories?post=20"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/tags?post=20"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}