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103年 - 103 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#120325
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10. Evaluate
cos(2nx)sinx dx, where n is an integer. (10 分)
其他申論題
a. Sketch the region of integration for the given iterated integral. (5 分)
#512571
b. Change or reverse the order of integration. In other words, rewrite the integral in the form of . (5 分)
#512572
8. The function f is defined by . Evaluate f(1). (10 分)
#512573
9. Find dr dθ. (10 分)
#512574
11. Evaluate dy dx. (10 分)
#512576
12. Find the least squares line for the given data. (10 分)(3,2), (4,3), (5,2). Method of Least Squares: The straight liney = a + bxshould be fitted through the given points (x₁,y₁), ..., (xₙ,yₙ) so that the sum of the squares of the distances of those points from the straight line is minimum, where the distance is measured in the vertical direction (the y-direction).
#512577
(a) (5 分)
#512578
(b) (5 分)
#512579
(c) (5 分)
#512580
(a) (5 分) y3+ 4xy - 3x2 = 2
#512581
cos(2nx)sinx dx, where n is an integer. (10 分)
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cos(2nx)sinx dx, where n is an integer. (10 分)