96年 - 96 國立成功大學轉學生招生考試試題_全校:微積分#114289

1. Show that tan^-1+ tan^-1 x = C, where C is a constant.
 And fnd the value of C. (Note: tan^-1 x = arc tan x) (10%)

2. Find the convergence set for the power series

and also find its sum. (10%)

3. Find the average value of f(x) = tan^-1on the interval [0,2]. (10%)

7. The function f(x,y) = 6x² -8x + 2y² - 5 is continuous on the closed region R defined by x² + y² ≤1. Find its absolute extrema over R. (10%)

(a) find equations of the tangent lines to the graph at the points corresponding to x =  ； (5%)

(b) also find for the equation in (a) for those points corresponding to x = .  (5%)

9. Compute dA, where R is the region bounded by the R graphs of y= x, y= x -π, y = -3x + 3, and y = -3x + 6. (10%)