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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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2. (5%) Let
dt, find derivative of F(x) .
其他申論題
6. (10 points) Let fn:[0,1] →R, , be a sequence of increasing functions, i.e., fn(x) ≤fn(y) for all and n N. Assume that fn Sfnt1 and Ifn(x)I s 1 for all xe [0,1] and neN. Show that fn converges (pointwisely) to an increasing function.
#441518
7. (10 points) Can you find a C1 function f:R2 →IR such that Vf(x,y)= (-y,x) for all (x,y)? Find such a function or prove that it does not exist.
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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).
#441520
1. (10 %) Prove or disprove that.
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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
(a) (5%) Findxdx
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(b) (10 %) Evaluate the improper integral
#441526
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.
#441528
dt, find derivative of F(x) .
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dt, find derivative of F(x) .