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

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

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%)

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

(a)

(b)

(c)

 5. For k≥0 find=______ (5%) 

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

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

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

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