所屬科目:研究所、轉學考(插大)-微積分
1. (10 points) For what values of a and b, a,b≠0, is the following equation true?
(a) (5 points) Let f(x) = sec2 x on be the inverse function of f. Find ()'(4) =
(b) (5 points) Let f = f(x,y) be a differentiable function of r and y, and let x= rs,y =rts and h(r,s) = f(x,y) = f(rs,r+ s). Assume (1,2) = 2, (1, 1) =________
3. (10 points) If dt, on what interval(s) is f increasing?
4. (10 points) Let a > 0 be a constant. Evaluate
5. (10 points) Find the area of the region that lies inside the curve r = 4sinθ and outside the curve r = 2.
6. (10 points) For what real values of p does the series converges?
7. (10 points) Let f(x) be the function defined by the power seriesTry to express f(s) as an elementary function.
9. (10 points) Evaluate dA, where R is the region in the first quadrant bounded by lines y = x, y = 3x, and the hyperbolas xy = 1, xy = 3.
10. (10 points) Evaluate the line integral dy, where C is the arc of the the circle x2 + y2 = 4 traversed counter-clockwise from (2,0) to (-2,0).