![\lim_{x\rightarrow0}\frac{\sqrt[2]{x+2}+\sqrt[2]{x+6}-\sqrt[2]{6}-\sqrt[2]{2}}{x}](/latexrender/pictures/0b8f88826b60494555aa0310ddcfbe67.png "\lim_{x\rightarrow0}\frac{\sqrt[2]{x+2}+\sqrt[2]{x+6}-\sqrt[2]{6}-\sqrt[2]{2}}{x}")
Bom... eu multipliquei a função pelo divisor, e achei x², o que me permitiu "cortar" o x.
![\lim_{x\rightarrow0}\frac{x}{\sqrt[2]{x+2}+\sqrt[2]{x+6}-\sqrt[2]{6}-\sqrt[2]{2}}](/latexrender/pictures/e7280533690c9be7e849417293c208d5.png "\lim_{x\rightarrow0}\frac{x}{\sqrt[2]{x+2}+\sqrt[2]{x+6}-\sqrt[2]{6}-\sqrt[2]{2}}")
Porém, mesmo assim eu não posso substituir x por 0, pois ainda assim meu denominador vai igualar a 0.
Desde já agradeço pela ajuda.
por AlexanderCanust » Seg Abr 27, 2015 20:37
por AlexanderCanust » Ter Abr 28, 2015 19:40
Voltar para Cálculo: Limites, Derivadas e Integrais
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![\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}](/latexrender/pictures/981987c7bcdf9f8f498ca4605785636a.png "\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}")
![\sqrt[]{2}](/latexrender/pictures/f21662d1cabab6e8b273a4b6f1cd663a.png "\sqrt[]{2}")
(dica : igualar a expressão a 
e elevar ao quadrado os dois lados)![L=\lim_{x\rightarrow 0}(\sqrt[]{x+2}-\sqrt[]{2})/x+\lim_{x\rightarrow 0}(\sqrt[]{x+6}-\sqrt[]{6})/x](/latexrender/pictures/74481601468cae0d183a34bb74996c3a.png "L=\lim_{x\rightarrow 0}(\sqrt[]{x+2}-\sqrt[]{2})/x+\lim_{x\rightarrow 0}(\sqrt[]{x+6}-\sqrt[]{6})/x")
![=\lim_{x\rightarrow 0}(\sqrt[]{x+2}-\sqrt[]{2}).(\sqrt[]{x+2}+\sqrt[]{2})/(x.(\sqrt[]{x+2}+\sqrt[]{2}))+\lim_{x\rightarrow 0}(\sqrt[]{x+6}-\sqrt[]{6}).(\sqrt[]{x+6}+\sqrt[]{6})/(x.(\sqrt[]{x+6}+\sqrt[]{6}))](/latexrender/pictures/a32b83804f176ac20c39322d8f3a3abb.png "=\lim_{x\rightarrow 0}(\sqrt[]{x+2}-\sqrt[]{2}).(\sqrt[]{x+2}+\sqrt[]{2})/(x.(\sqrt[]{x+2}+\sqrt[]{2}))+\lim_{x\rightarrow 0}(\sqrt[]{x+6}-\sqrt[]{6}).(\sqrt[]{x+6}+\sqrt[]{6})/(x.(\sqrt[]{x+6}+\sqrt[]{6}))")
![=\lim_{x\rightarrow 0}x/(x.(\sqrt[]{x+2}+\sqrt[]{2}))+\lim_{x\rightarrow 0}x/(x.(\sqrt[]{x+6}+\sqrt[]{6}))=\lim_{x\rightarrow 0}1/(\sqrt[]{x+2}+\sqrt[]{2})+\lim_{x\rightarrow 0}1/(\sqrt[]{x+6}+\sqrt[]{6})](/latexrender/pictures/2c604e19b61f30fccc7617d2e61b03f0.png "=\lim_{x\rightarrow 0}x/(x.(\sqrt[]{x+2}+\sqrt[]{2}))+\lim_{x\rightarrow 0}x/(x.(\sqrt[]{x+6}+\sqrt[]{6}))=\lim_{x\rightarrow 0}1/(\sqrt[]{x+2}+\sqrt[]{2})+\lim_{x\rightarrow 0}1/(\sqrt[]{x+6}+\sqrt[]{6})")
=![=1/(2\sqrt[]{2})+1/(2\sqrt[]{6})](/latexrender/pictures/1baecb1d509eaed56632e8109eecb27d.png "=1/(2\sqrt[]{2})+1/(2\sqrt[]{6})")
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