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97年 - 97 台灣聯合大學系統(清、交、陽、中四校聯招)學士班轉學生聯合招生試題：微積分#113210
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4. Evaluate the integral
Answer : ____________
其他申論題
10. Solve the differential equation xy' = y + x2 sin x with y(π) = 2π.
#483657
1. If f'(0) =-1, find.Answer : ________
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2. Find dt. Answer:_________
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3. Convert the integral dzdydx to an equivalent integral in cylindrical coordinates. Answer :__________(Do not evaluate the integral).
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5. Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y- z = 0. Answer :__________
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6. The derivative of f(x, y) at P0(1, 2) in the direction of i + j is and in the direction -2j is -3. What is the derivative of f in the direction of -i -2j?Answer :__________
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7.the area of cap cut from the sphere x2 + y2 + z2 == 2 by the cone z =.Answer :__________
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8. Evaluate the line integral f where C consists of line segments joining successively the points (1,0), (I, 1), (-1, 1) and (-1,0). Answer : __________
#483665
(a) Show that f'(0)=0.(6分)
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(b) Is the derivative function f'(x) continuous at x= 0? Explain. (6 分)
#483667
Answer : ____________
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Answer : ____________