Cálculo Diferencial e Integral:Disponha Cálculo: Lista

CAI- Limite Indeterminado 2 :Lista de Exercício

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Calcule os seguintes Limites

$\mathrm{} \displaystyle\lim_{ x \to 0 } \displaystyle\frac{ \sqrt{1+x} - 1}{x} $

$\mathrm{} \displaystyle\lim_{ x \to 0 } \displaystyle\frac{\sqrt{2x+1}-3}{\sqrt{x-2}-\sqrt{2}} $

$\mathrm{} \displaystyle\lim_{ x \to 1 } \displaystyle\frac{\sqrt[3]{x}-1}{\sqrt{x}-1} $

$ \displaystyle\lim_{ \xi \to \infty } \left( 1+\displaystyle\frac{1}{\xi} \right)^{\xi+5}$

$ \displaystyle\lim_{ \varphi \to \infty } \left\{ \varphi[ \ln{(\varphi + 1)} -\ln{(\varphi)} ] \right\} $

$ \displaystyle\lim_{ x \to \displaystyle\frac{\pi}{2} } \left( 1+\cos(x)\right)^{3\mbox{sec}(x)} $

$ \displaystyle\lim_{ x \to 0 }\displaystyle\frac{ \ln{(1+\alpha x)} }{x} $

$ \displaystyle\lim_{ x \to \infty } \left( \displaystyle\frac{2x+3}{2x+1} \right)^{x+1} $

$\displaystyle\lim_{ x \to 0 } \left( 1+3\mbox{tg}^{2}(x) \right)^{\mbox{cotg}^{2}(x) } $

$ \displaystyle\lim_{ \varphi \to \infty } \displaystyle\frac{ \ln{(1+e^{\varphi})}}{\varphi} $

$ \displaystyle\lim_{ \varphi \to \displaystyle\frac{\pi}{2} } \displaystyle\frac{ \ln{(\mbox{sen}(\varphi))}}{(\pi -2\varphi)^{2} } $

$\displaystyle\lim_{ \varphi \to \infty } \displaystyle\frac{ \ln{(\varphi)}}{\varphi^{n}} $ ( Em que $n>0$ )

$ \displaystyle\lim_{ \varphi \to \infty } \displaystyle\frac{ \ln{\left( 1+\displaystyle\frac{1}{\varphi} \right)}}{\mbox{arccotg}(\varphi) } $

$\displaystyle\lim_{ \varphi \to \infty } \displaystyle\frac{ \ln{\displaystyle\left(\frac{\varphi+1}{\varphi} \right) }} {\ln{\displaystyle\left(\frac{\varphi-1}{\varphi} \right)}} $

$\displaystyle\lim_{ \varphi \to 0 } \left[ \varphi- \varphi^{2}\displaystyle\ln{\left(1+\displaystyle\frac{1}{\varphi}\right)} \right] $

$ \displaystyle\lim_{ \varphi \to 1 } \left[ \mbox{tg}\left( \displaystyle\frac{\pi \varphi}{4}\right)^{\mbox{tg}\left( \displaystyle\frac{\pi \varphi}{4}\right)} \right] $

$\displaystyle\lim_{ \varphi \to 0 } \displaystyle\frac{ \ln^{2}{(1+\varphi)} - \mbox{sen}^{2}(\varphi)} {1-\displaystyle e^{-\varphi^{2}}} $

Lista - Limite Indeterminado 2 ( f)