99年 - 99 國立臺灣師範大學_學士班轉學生招生考試試題_物理系二年級：微積分#122249

1. sinx = (A)-1(B) 0 (C) 1 (D) Not exist

2. The total number of vertical asymptotes of the graph of is (A) 1 (B) 2 (C) 3 (D) 4

3. Find the limit: = (A) -1 (B)∞(C) -∞ (D) 1

4. The integral dx= (A) 0 (B)∞ (C) -∞ (D) Doesn't exist.

5. Which of the following statement is TRUE? (A) xf(x)dx = f(x)dx when f is continuous on [a, b]. (B) when f is continuous on [a, b] and f(x) ≥ 0 for all x ∈ [a, b]. (C) If f and g are differentiable and 0<f(x) ≤ g(x) on [a, b] then f'(x) ≤ g(x). (D) If f and g are continuous and 0< f(x) ≤ g(x) on [a, b] then f(x)dx≤g(x)dx.

6. The centroid of the region bounded by the curve y = cosx, y = 0, x = 0, and x = is (A) (B) (C) (D)

7. Let y = dt. At what value of t does the local maximum of y occur? (A) 0 (B) 1 (C) -1 (D) 2 (E) -2

8. Let f(x) =(x - 1). Which of the following is NOT true? (A) f has an inflection point at x = . (B) f has a relative maximum at x = 0. (C) f has a relative minimum at x = . (D) f(x) → -∞ as x → -∞

9. If f(x) = x•e^x - 2x ln x², then which one of the following functions is an anti-derivatives of f(x)? (A) (B) (C) (D)

10. To find the surface area of the solid of revolution formed by rotating y = x² over [0, 2] about the x-axis, we must evaluate (A) (B) (C) (D)

1.- 3x) =__(1)__.

4. Suppose F(x) = dt and x ≥ 0. Find (F^-1)'(0) = (4) ______

5. Find the tangent line to y= e^2x and contains the point (, 0). __(5) __.

6. dx =__ (6)__.

7. Find the arc length of the curve y² = x³ from (0, 0) to . __(7)__.

8.=__ (8)__

9. dy dx =__ (9) __.

2. Find the volume of a cap of a sphere with radius r and height h.