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研究所、轉學考(插大)-微積分
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92年 - 92 國立暨南大學轉學生招生考試試題_微積分_(資工系)#124709
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5. (20%) Verify that the series
has interval of convergence [-1, 1].
其他申論題
(a) (12%) Prove that ln(ab) = ln(a) + ln(b) for a, b ＞ 0.
#530535
(b) (8%) By (a), to prove ln(1/b) = -ln(b) and ln(a/b) = ln(a) - ln(b).
#530536
(a) (8%) Find the area of the region R bounded by the graph of f and thex-axis.
#530537
(b) (12%) Find the volume of the solid generated by revolving R around thex-axis.
#530538
1. Prove: If f is the function defined by thendoes not exist. (10 points)
#530540
(a) Findfor y = (x3+ 1)(3x² + 2x - 1). (10 points)
#530541
(b) Find (). (10 points)
#530542
(c) Find，hint: sec²x - tan²x = 1. (10 points)
#530543
3. The number is a root of the equation x² - 3 = 0. Please estimateby applying the Newton-Raphson method to the functionf(x) = x² - 3 starting at x₁ = 2. Hint: the Newton-Raphson formula is. (10 points)
#530544
4. Find f to satisfy that f '(x) = 6x - 2, f'(1) = -5, and f '(1) = 3. (10 points)
#530545
has interval of convergence [-1, 1].
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has interval of convergence [-1, 1].