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110年 - 110 國立中山大學碩士暨碩士專班招生考試_應數系碩士班/乙組:微積分#104294
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題組內容
5.
(a) (5%) Find
xdx
其他申論題
1. (10 %) Prove or disprove that.
#441521
2. (5%) Letdt, find derivative of F(x) .
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3. (10%) Use Riemann sum to find the definite integraldx.
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4. (10 %) Find , where a, b are constant real numbers.
#441524
(b) (10 %) Evaluate the improper integral
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6. (10 %) State the Integral Test and apply it to determine the convergence or divergence of the series:
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7. (20 %) Find the length of r = 1 + cos θ and area of its interior region.
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8. (10 %) Find the volume of the solid inside both x2 + y2 + z2 = 36 and (x - 3)2 + y2 = 9.
#441529
9. (10 %) Use the change of variables to evaluate the given double integral where R is the region given in the picture on the right.
#441530
1.解下列微分反應方程式:(15%)
#441531