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

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

(b)y=dt.

(c) y = cos^-1(2x+1).

(d) y = tanh(1 +e^2x).

2. (5%) Find (f^-1)'(2) if f(x) = 1 + 2x + e^x.

3. (25%) Sketch the graphs of .
(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 dx.

5. (10%) Given the power series， (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 =.

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

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