107年 - 107 國立臺北大學_轉學生招生考試試題_通訊工程學系二年級：微積分#118609

1. (12%) Compute xdx.

2. (12%) Find the area enclosed by the equation .

3. (12%) Compute dx.

4. (14%) Use Simpson's rule with n=10 to approximately compute

1. (8%) Prove that lim_x→2(3x-1)= 5.

2. (8%) Show that the function is continuous on the interval [-2,2].

3. (8%) Show that the function f(x) = x² -x + 1 is differentiable for

4. (8%) Suppose that f(0) = 0 and f'(x) ≥6 for . How small can f(100) possibly be?

(Hint: the Mean Value Theorem)

5. (6%) Find y' if x⁴ +y⁴ =8xy².

6. (6%) Find y' if y = cos(xcos x).

7. (6%) Find y' if