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研究所、轉學考(插大)-微積分
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100年 - 100 國立暨南國際大學轉學生入學考試試題_資工系二：微積分#124207
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4. (10%) Use polar coordinates to calculate the volume of a sphere of radius R.
其他申論題
(b) (5%) Let g be a function of several variables which is defined in some neighborhood of 0. We will say that g(h) is o(h) iff = 0.Prove that g(h) = ||h|| is o(h).
#527958
(c) (5%) Let g(x,y)=x²+ y², prove that ∇g(x, y) = (2x,2y) by the definition g(x+h) - g(x)= ∇g(x) ⋅ h + o(h).
#527959
2. (15%) Suppose that the temperature at each point of a metal plane is givenby the function T(x,y)=1+x²-y². Find the path followed by a heat-seekingparticle that originates at (-2, 1).
#527960
3. (10%) Find the directional derivative of the function g(x,y)=x²+y² at thepoint (1, 2) in the direction of the vector 2i-3j.
#527961
5. (10%) Find the interval of convergence of Σ(x+2)k.
#527963
6. (10%) Sketch the graph of the function f(x) = - 5x.
#527964
7. (10%) Evaluate: ∫.
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8. (10%) Estimate f(5.4) given that f(5)=3 and f'(x) =.
#527966
9. (10%) The region bounded by the curves y = x²-2x and y = 3x is revolvedaround the line y = -1. Find the volume of the solid that is generated.
#527967
(1)
#527968
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