103年 - 103 國立臺北大學_學士班暨進修學士班轉學生招生考試試題_資訊工程學士、通訊工程學系學士班二年級：微積分#119732

科目：研究所、轉學考(插大)-微積分 | 年份：103年 | 選擇題數：0 | 申論題數：23

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 (23)

1. If f(x)=x²+x for (2) = __(la) (1%)__ and f(f^-1(I)) =__(1b) (1%)__

2. Express the following function p(x) in the form of f。g。h

Constraints: functions f, g, h are exponential, power, and linear functions, respectively. Find f(x) =__(2a) (1%)__, g(x)= __(2b) (1%)__, h(x)=__(2c) (1%)__

3.Ifs(x)=x³+=__(3) (4%)__.

4.=__(4)(2%)__

5. = __(5) (3%)__

(a) domain= __(6a) (1%)__

(b) first derivative, i.e. f'(x)=__(6b) (2%)__

(c) critical numbers are __(6c)(1%)__

(d) horizontal or/and vertical asymptotes are __(6d) (2%)__

(e) intervals of increasing or/and decreasing are __(6e) (2%)__

(f)) refection points(p,f(p)), where p =__ (6f) (2%)__

(g) intervals of concaving upward or downward are __(6g) (2%)__

(h) local or absolute maximum/minimum (s) are__(6h) (2%)__

(i) range= __(6i) (2%)__

Ⅱ 、計算題(計算過程列入計分,並標註最後答案)
7.If f(x)=(2014x⁶+2x+8)^x,find f'(x).(5%)

8.if f(x)=dt,find f'(x). (5%)

9. Evaluate dx (5%)

10. Find to the 1-st decimal place by the Newton's method with an initial guess of x₀ =4. (5%)

Ⅲ、

11. Calculatc the itegm

12. Find the volume of the given solid under the surface z = xy and above the triangle with vertices (1, 1), (4, 1), and (1, 2). (10%)

13. Find the volume of the parallelepiped determined by vectors a =i+ j-k, b=i-j+k, c=i+j+k. (10%)

14. Find the Maclaurin series of the function and its radius of convergence. (10%)

15. Evaluate the integral for by making an appropriate change of variables, where R is given by the inequality |xl+ly |≤1.(10%)