99年 - 99 國立成功大學轉學生招生考試試題_全校:微積分#114206

科目：研究所、轉學考(插大)-微積分 | 年份：99年 | 選擇題數：0 | 申論題數：14

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (14)

(a) Find the asymptotic lines of the graph y = f(x), if exist. (6%)

(b) Find the absolute extreme values of f, if exist. (8%)

(a)show that(8%)

(b)What is the domain of E(x) ? Explain your answer. (4%)

3. Let f(x) =∫₀^xxcos(t²)dt.Find f'(0) and f"(0). (10%)

(a) change the order of integration to be dydx;(6%)

(b) and then evaluate the integral.(8%)

(a) Find the critical points of f(x,y). (6%)

(b) Determine whether the critical points are points of maximum, minimum values or saddle points. (8%)

(a) use z = Inx to transform such an equation into an equation with constant coefficients;(6%)

(b) find the general solution of (a) in terms of x. (6%)

7. Let the function z = f(x -y,y- x). Prove that (10%)

(a) List the double integral to find the volume of Q using polar coordinate system. (6%)

(b) Evaluate the double integral at (a). (8%)