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

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}

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

已知$f(x)=\int_{0}^{x}e^{\sqrt{t}}\,dt$，求$f(1)=$(）. A. 0B. 0C. 1D. $e$E. $e^{-1}$

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

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}{

注 类似地，求极限$\lim_{x \to 0} \frac{\ln(1+x)\ln(1-x)-\ln(1-x^2)}{x^4}$. 注 类似地，求极限$\l

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

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

求不定积分 $\int \frac{\sin^2 x \cos x}{1 + 4\sin^2 x} dx$. 求不定积分 $\int \frac{\sin^2

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