91年 - 91 中原大學_轉學生入學招生考試_理、工學院二年級_應用數學系：微積分#124602

1.(a)=________

(b)=________

2. The equation of the normal line for x³-xy+3y²=3 at  is _________

3. Let x² sin(x²)=, then =_________

4. The directional derivative of f(x,y,z)= at (1,2,-2) in the direction of the path is ________

二、計算題
1. Evaluate .

2. Sketch the graph of f(x)=.

3. Evaluate .

4. Find the length of the curve y= between x=0 and x=1.

5. Find the area bounded by the cardioid(心臟線) r=1-cosθ.

6. Determine whether the series is convergent or divergent.

7. Let
Sketch the region Ω that gives rise to the repeated integral, and then evaluate it.