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104年 - 104 國立臺灣師範大學_學士班轉學生招生考試試題_機電工程學系二年級：微積分#118783
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8. In which directions does the directional derivative of the function f at point (1,1)vanish if f(x,y)=x
2
+2y
2
?(10分)
其他申論題
4. Evaluate the integral, ∫(x2 -2)exp(x3 -6x)dx, in which exp(●) denotes the natural exponential function.(10 分)
#506405
5. Find the volume under the surface z=exp(-x-y) and above the triangle with vertices (0,0),(1,0),and (0,1).(10分)
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6. Find the Taylor series of the function f(x)=In(x) about x=1, in which In(●) denotes the natural logarithmic function. Moreover, find the radius of convergence and the interval of convergence for this series.(10分)
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7. Evaluate the integral, exp(-x)sin(x)dx.(10分)
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9. Find. (10分)
#506410
10. Evaluate the integral, cos(2nx) sin(x)dx, where n is an integer. (10 分)
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(1) (7 points)
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(2)(8 points)
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(3) ∫cos(2θ)cos(3θ)dθ (7 points)
#506414
(4) (8 points)
#506415
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