Chia-Chung We>試卷(2022/09/23)

# 100 年 - 100 國立中興大學轉學考招生考試試題_化學、物理、資工、土木二年級:微積分#110877

【非選題】
1.
1. Suppose that f(x) and g(x) are differentiable functions, and the following information is known about them: f(2)=-1,f'(2)=5,8(2)=1,g'(2)=2,8(0)=2,g'(0)=4

【題組】

(a) If , compute F'(2)= __________ (5%)

【非選題】
2.【題組】(b) If G(x)=x3f(x)-7g(x) ,compute G'(2)=_________ (5%)

【非選題】
3.

2. Two curves intersect orthogonally when their tangent lines at each point of intersection are perpendicular. Suppose C is a positive number. The curves intersect twice. Find C so that the curves intersect orthogonally. (5%)

【非選題】
4.

3. Please state "Mean Value Theorem for Derivatives" and show that| sinx-siny|≤s|x-y|. (10%)

【非選題】
5.
4. Evaluate the following integrals: (15%)

【題組】

(a)

【非選題】
6.【題組】

(b)

【非選題】
7.【題組】

(c)

【非選題】
8.

5. For k≥0 find=______ (5%)

【非選題】
9.6. Find the volume of the solid generated by revolving the region in the circle (x-3)2+(y- 4)=4 about y=-x. (10%)

【非選題】
10.

7. The position vector of a particle at time t≥ 0 is(a)ds/dt=_______(b)aT=______ (c) aN =_______(10%)

【非選題】
11.8. Given that fx(1,3)=4 and fy(1,3)=-7, find the directional derivative of f at (1,3) in the direction toward (6,15). (10%)

【非選題】
12.

9. Find the limit =_________(5%).

【非選題】
13.

10. The maximum values of f(x,y)=y2 -x2 on the ellipse =1is________(10%)

【非選題】
14.

11. Find the integral drdx=________(10%)

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