108年 - 108 國立臺灣大學轉學生招生考試試題_(商、管、農、經學院聯招) ：微積分(C)#113211

1 Lemniscate (x² + y²)² = x² -y² At the point (x,y)= dy/dx=?

2. If x³+y³= 3xy, then x + y≤max = ?

3. The probability density function of an exponential distribution is f(x) = if x ≧ 0, f(x) = 0 if x ＜ 0. Find the expected value E(x) = ?

4.f(x) = = ?

5. f(x) = 1/(x² - x-2) = Taylor series ==?

7. = ?

8. Find the area of the surface z = xy, x² + y² ≦ 1.

10. Polar coordinate x = r cosθ , y = r sineθ. Cardioid r = 1 - sinθ . At the point (x,y)=(1,0) d²y/dx²=?