108年 - 108 國立高雄師範大學學士班轉學生招生考試試題_數學系及光通系二年級：微積分#116353

(1). A contnuous function f (x) is differentiable

(2). If a function is differentiable at a point, then it is continuous at that point.

(3). Let f (x) be a differentiable function. Then f '(x) must be continuous.

(4). The absolute function f(x)=|x| is continuous at x=0.

(5). The absolute function f(x)=|x| is differentiable at x=0.

(6). f '(c)= 0 implies f (c) is an extreme value.

2. （10％）Find the Maclaurin series of e^x .

3. （10％）Find the global maximum and minimum values of x²+y²+2 on .

(a)

(b)

5. （15％）Evaluate the integral if C is a piecewise smooth simple closed curve oriented counterclockwise such that (a) C does not enclose the origin and (b)C encloses the origin.

6. （15％）Use the transformationu=xy ,v=x²-y² to find where R is the region in the first quadrant that is enclosed by the hyperbolas x²-y²=1,x²-y²=4 and the circles x²+y²=9 , x²+y²=16.

108年 - 108 國立高雄師範大學學士班轉學生招生考試試題_數學系及光通系二年級：微積分#116353

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