105年 - 105 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#145937

1. Find the limit (if possible): .

2. Let be the function given by. Find all values of and so that is differentiable at .

4. Decide whether the series converges or diverges: .

5. Find the open intervals on which the function is increasing.

6. Find the equation of the tangent line to the graph of the function at .

7. Find a function that satisfies the differential equation and the initial condition

8. Find the indefinite integral .

9. Let be the function given by (a) Compute the gradient of at the point .

(b) Find the equation of the tangent plane to the surface at the point

10. Find the area of the region R that lies below the parabola above the x-axis, and above the line .