110年 - 110 國立清華大學碩士班考試入學試題_科技管理研究所／乙組：微積分#105239

(b) If . Ans:_________

(c) Find the indeinite integraldx.. Ans:__________.

(d) Find the indeinite integral xdx. Ans:___________

(e) Evaluste the double integral. Ans:__________

(f) Solve the initial-value problem: Ans:_____________

2. (9 pts) For what values of the constants a and b is a point of infection of the curve
 y = an + bsin g + cos x ?

3. (10 pts) Determine whether the series

 is convergent or divergent.

(a) Show that

(b) Show that

5. (12 pts) If the ellipse is to enclose the circle x²+ y² = 2y, what values of a and b mininize the area of the ellipse ?

(a) Show that the function
  
is monotone decreasing on (1,∞).

(b) Find .