A
一、求下列极限(5 X 4 = 20 分)
1. $\displaystyle \lim_{x\to\infty}(\frac{2x+3}{2x-3})^{3x+2}$
2. $\displaystyle\lim_{x\to0} \frac{x-\arcsin x}{\sin x^3}$
3. $\displaystyle \lim_{x \to 0} (1 - \frac{x^2}{2})^{\frac{1}{\sin^2 x}}$
4. $\displaystyle\lim_{x\to x^{0^+}} \frac{\int_{0}^{x^2}t^{\frac{3}{2}}dt}{\int_{0}^{x}t(t-\sin t)dt}$
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