95年 - 95 國立暨南國際大學_轉學生入學考試試題_電機系二：微積分#124710

1. Prove: If f is the function defined by thendoes not exist. (10 points)

(a) Findfor y = (x³+ 1)(3x² + 2x - 1). (10 points)

(b) Find (). (10 points)

(c) Find，hint: sec²x - tan²x = 1. (10 points)

3. The number is a root of the equation x² - 3 = 0. Please estimateby applying the Newton-Raphson method to the function
f(x) = x² - 3 starting at x₁ = 2. Hint: the Newton-Raphson formula is
. (10 points)

4. Find f to satisfy that f '(x) = 6x - 2, f'(1) = -5, and f '(1) = 3. (10 points)

(a) Find . (10 points)

(b) Compute dx. (10 points)

(a) Calculate the angle between a and b. (5 points)

(b) Find proj，a . (5 points)

7. Find an equation f(x, y, z) = 0 for the plane that passes through the point P(-2, 3, 5) and is perpendicular to the line l with scalar parametric equations: x = -2 + t, y = 1 + 2t, z = 4. (10 points)