101年 - 101 國立嘉義大學_碩士班(乙組)招生考試試題_企業管理學系：應用微積分#146363

1. (a) Please evaluate the function .(5%)

(b) Please find the derivative of the function . (5%)

2. If an initial amount A₀ of money is invested at an interest rate γ compounded n times a year, the value of the investment after t years is .
If we let n →∞, we refer to the continuous compounding of interest. Use L’Hospital’s Rule to show that if interest is compounded continuously, then the amount after n years is .(20%)

3. (a) If , please find y_n.(5%)

(b) Please evaluate .(5%)

4. Please find the Taylor series for about 1, and determine the radius of convergence for this series. (10%)

(a) Given k1=8; k2=7; k3=6; find (x, y) such that f is minimum. (Remember to check the 2^nd order condition).

(b) Given a plan that is defined by 3x-5y+2z=150, where z is defined as above. Let , find , , .

6. (a) Find the Taylor series for centered at x=0.(5%)

(b) Find .(5%)

7. Let , find .(10%)

8. If , find a and b. (10%)