Chia-Chung We>試卷(2022/09/19)

# 111 年 - 111 台灣綜合大學系統學士班轉學生聯合招生試題：微積分A(理工組二年級)#110842

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1. (10 points) For what values of a and b, a,b≠0, is the following equation true? 【非選題】
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(a) (5 points) Let f(x) = sec2 x on be the inverse function of f. Find ( )'(4) =

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(b) (5 points) Let f = f(x,y) be a differentiable function of r and y, and let x= rs,y =rts and h(r,s) = f(x,y) = f(rs,r+ s). Assume (1,2) = 2, (1, 1) =________

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3. (10 points) If dt, on what interval(s) is f increasing?

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4. (10 points) Let a ＞ 0 be a constant. Evaluate 【非選題】
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5. (10 points) Find the area of the region that lies inside the curve r = 4sinθ and outside the curve r = 2.

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6. (10 points) For what real values of p does the series converges?

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7. (10 points) Let f(x) be the function defined by the power series Try to express f(s) as an elementary function.

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9.8. (10 points) Find the global maximum and global minimum of f(x, y, z) = x2+y2+z2 on the surface x2 + 2y2 + 3z2 = 1 by using the method of Lagrange multipliers.

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9. (10 points) Evaluate dA, where R is the region in the first quadrant bounded by lines y = x, y = 3x, and the hyperbolas xy = 1, xy = 3.

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10. (10 points) Evaluate the line integral dy, where C is the arc of the the circle x2 + y2 = 4 traversed counter-clockwise from (2,0) to (-2,0).

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