106年 - 106 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、通訊工程學系二年級(學士班)：微積分#116792

科目：研究所、轉學考(插大)-微積分 | 年份：106年 | 選擇題數：0 | 申論題數：10

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 (10)

(a) cos(xy) = 1 + sin y.

(b)y=651b7b5ddb46c.jpgdt.
(c) y = cos-1(2x+1).
(d) y = tanh(1 +e2x).
2. (5%) Find (f-1)'(2) if f(x) = 1 + 2x + ex.

3. (25%) Sketch the graphs of 651b7bc22e0cf.jpg.
(You need to describe (a) domain, (b) intercepts, (c) asymptotes (horizontal and vertical if any), (d) intervals of increasing and decreasing, (e) local maximum and minimum values, (f) interval of concavity, (g) points of iniection and (h) sketch the curve.)

4. (10%) Evaluate the integral 651b7c13686b5.jpgdx.

5. (10%) Given the power series651b7ca9ca76d.jpg， (a) find the series' radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally?
6. (15%) Use the method of Lagrange multipliers to find the maximum and minimum values of x2 + y2 subject to the constraint x2 - 2x + y2 - 4y = 0.

7. (15%) Find the area of the region R enclosed by the lines y = x - 2 and y = -x and the curve y =651b7cfe8aa27.jpg.