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研究所、轉學考(插大)-微積分
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96年 - 96 國立暨南國際大學_轉學生入學考試試題_資工系二:微積分#124712
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4. (10%) Find the area enclosed by the ellipse (x²/a²)+(y²/b²)=1.
(Hint: cos²x=(1+cos2x)/2.)
其他申論題
10. Determine the convergence or divergence of the following series, and state the test used:
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1. (15%) Sketch the graph of the function f(x) =.
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2. (15%) Find .[Hint: limit of Riemann sums]
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3. (10%) Calculate ∫eˣcosx dx. Hint: cosxdx=dsinx & integration by parts
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5. (10%) Let Show that g(x,y) does not exist.
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(a) (5%) Find giventhat x(t) = t and y(t) = t2. (These functions parameterize the parabola y=x2)
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(b) (5%) Find giventhat x(t) =1/4(t+4) and y(t) = t. (These functions parametrize the line y=4x-4)
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(c) (5%) Compute the directional derivative of f at (2,4) in the direction of i + 4j.
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(d) (5%) Notice that i + 4j is a direction vector for the line y=4x-4 and this line is tangent to the parabola y=x2 at (2,4). Explain why the computations in ( a ), ( b ), and( c ) yield different values.
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7. (10%) Show that the series converges on [-1,1).
#530570
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