101年 - 101 國立臺灣師範大學_學士班轉學生招生考試試題_數學系二年級：微積分#122185

1. (10 points) Find the limit lim_h→0.

2. (10 points) Is the function

differentiable at x = 0?

3. (10 points) Evaluate the integral dx.

4. (10 points) Does the improper integral dx converge?

(a) (10 points) Write down the equation of the tangent plane of σ at the point (3/2, 3/2, 3/).

(b) (25 points) Suppose a vector field (x, y, z) = is defined over the surface σ of H. Let denote the outward unit normal vector of σ. Evaluate the integral ∫∫_σdS.