103年 - 103 國立嘉義大學_碩士班(甲組)招生考試試題_應用數學系：微積分#146082

(a) .

(b) .

2. Let the function .
Find the constant k so that f is continuous at 2.

3. Find the area of the region bounded by the parabola y=x²-3x+3 and the line y=2x-3.

4. Find the absolute maximum and minimum of the function
f(x,y)=x²-3x+2y2+5 on the set

6. Find the local extrema of .

7. Use the Ratio Test and the fact that to show that converges.

8. Show that is continuous but not differentiable at (0,0).

9. Find the volume of the region bounded by ,z=4x²+4y² , z=0, x²+y²=1 and x²+y²=2.

10. Let the region R be bounded by y=4x+2, y=4x+5,y=3-2x and y=1-2x. Evaluate the double integral .