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研究所、轉學考(插大)-微積分
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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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4. (10 %) Find
, where a, b are constant real numbers.
其他申論題
8. (10 points) Construct a function f:R2 →IR such that fx and fy exist at (0,0) but f is not differentiable at (0,0).
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1. (10 %) Prove or disprove that.
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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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(a) (5%) Findxdx
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(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.
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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
, where a, b are constant real numbers.
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, where a, b are constant real numbers.