$\lim _{x \rightarrow 0^{-}} e^{\frac{1}{x}}=\_\_\_\_\_\_\_\_.$

$\lim _{x \rightarrow 0}(1-\sin 2x)^{\frac{1}{x}}=\_\_\_\_\_\_.$ $\lim _{x \rig

$\lim _{x \rightarrow \infty} x^{2}\left(2-x \sin \frac{1}{x}-\cos \frac{1}{x}\r

[例1] (2004) $\lim _{x \rightarrow 0}\left(\frac{1}{\sin ^{2} x}-\frac{\cos ^{2}

求极限 $\lim _{x \rightarrow +\infty}\left(x+e^{x}\right)^{\frac{1}{x}}$. 求极限 $\li

求极限 $\lim_{x \to 0} \frac{e^x \sin x - x(x+1)}{\sin^3 x}$. 求极限 $\lim_{x \to 0}

$\lim _{n \rightarrow \infty}\left[\left(1+\frac{1}{n}\right)\left(1+\frac{2}{n}

给出以下4个极限① $\lim_{x \to 1} \frac{x}{e^{x-1}}$.② $\lim_{x \to 0} \arctan \frac{1}{

$\lim_{{x \to \infty}} (\sqrt[3]{x^3 + x^2} - xe^{\frac{1}{x}}) = \_\_\_\_\_\_.$

已知 $f(x) = \lim_{n \to \infty} \frac{\ln(e^n + x^n)}{n}$, $(x > 0)$.(1) 求 $f(x)$

求极限 $\lim_{x \to 0} \frac{\int_{0}^{x} \sin t^{2} dt}{x - \arctan x}$. 求极限 $\li