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研究所、轉學考(插大)-微積分
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107年 - 107 國立臺北大學_轉學生招生考試試題_電機工程學系二年級：微積分#118643
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1. (12%) Compute
xdx.
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4. (8%) Suppose that f(0) = 0 and f'(x) ≥6 for . How small can f(100) possibly be?(Hint: the Mean Value Theorem)
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5. (6%) Find y' if x4 +y4 =8xy2.
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6. (6%) Find y' if y = cos(xcos x).
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7. (6%) Find y' if
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2. (12%) Find the area enclosed by the equation
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3. (12%) Compute dx.
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4. (14%) Use Simpson's rule with n=10 to approximately compute
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二、1. (8%) Prove that limx→2(3x-1) = 5.
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2. (8%) Show that the function is continuous on the interval [-2,2].
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3. (8%) Show that the function f(x) = x2 - x + 1 is differentiable for
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xdx.
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xdx.