94年 - 94 台灣聯合大學系統(清、交、陽、中四校聯招)學士班轉學生聯合招生試題：微積分#113222

1. xsinxdx=________.

2. For the equation  y³-xy²+cos(xy)=2 , at the point (0,1) is ______.

3. Let , where f iscontinuous and g and h are differentiable. Find F'(t)=___________.

4. The maximum value of f(x,y)=y²-x² on the ellipseis=_________.

5. dydx= _________.

6.=__________.

7. Let f :[0,3]→[0,3] be a continuous function with f(0)=0 and f(3)=3. If f is one-to-one and , then=________ ,where f^-1 is the inverse function of.

8. The radius of convergence of the power series is___________.

2. Prove that

3. Evaluatedy,where C is the unit circle.