所屬科目：研究所、轉學考(插大)-微積分
(a)\( \lim_{x \to 0} \frac{e^{2x} - 1}{x} \)
(b)\( \lim_{x \to \infty} \frac{\ln x}{x} \)
(a)\( \int xe^x dx \)
(b)\( \int \frac{4x}{x^2+9} dx \)
3. Find the absolute maximum and minimum values of \( f(x) = \sqrt{4 - x^2} \), \( -2 \le x \le 1 \) .
4. Show that there is a real root of the equation between x3+x-1=0 and 1.
5. Find a power series for f(x)=ln x, centered at 1, and determine the interval of convergence.
(b) .
7. Show that is continuous, differentiable at x= 0 and find the value of f(0).
8. Find the area between and from x=0 to .
9. Evaluate the following limits
阿摩線上測驗
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.
is continuous, differentiable at x= 0 and find the value of f(0).
and 
from x=0 to 
.