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95年 - 95 國立暨南國際大學_轉學生入學考試試題_電機系二：微積分#124710
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題組內容
2.
(a) Find
for y = (x
3
+ 1)(3x² + 2x - 1). (10 points)
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5. (20%) Verify that the serieshas interval of convergence [-1, 1].
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1. Prove: If f is the function defined by thendoes not exist. (10 points)
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(b) Find (). (10 points)
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(c) Find，hint: sec²x - tan²x = 1. (10 points)
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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)
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(a) Find . (10 points)
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(b) Compute dx. (10 points)
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for y = (x3+ 1)(3x² + 2x - 1). (10 points)
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for y = (x3+ 1)(3x² + 2x - 1). (10 points)