所屬科目：研究所、轉學考(插大)-微積分
(a) $\int\frac{xe^{2x}}{(2x+1)^{2}}dx$
(b) $\int_{1}^{3}\frac{3}{x^{2}-3x}dx$
(c) $\int_{-\infty}^{\infty}(x-u)\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(x-u)^{2}}{2\sigma^{2}}}dx$
2. Evaluate the double integral \( \int_{0}^{1} \int_{y/2}^{1/2} e^{-x^2} dx dy \) .Note that it is necessary to change the order of integration.
(a) Write a differential equation where the size y of the herd will follow the equation and t is measured in years. (10%)
(b) Then derive this logistic curve, find / solve for the constant of integration and the proportionality constant. (10%)
(c) How long will it take to establish a population of 150? (10%)
4. Find an equation of the tangent line to the graph of the function given below at the given point, x=0, and $f(x)=\left(\frac{x+5}{x-1}\right)(2x+1)$
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