109年 - 109 國立臺北大學_轉學生招生考試試題_通訊工程學系二年級：微積分#117924

1. (15%) Use the Lagrange multipliers to find the extreme values of f(x, y) = x² + 2y²on the circle x²+y²=1

2.(10%) Find y' if x^y = y^x.

(You need to describe (a) domain, (b) intercepts, (c) asymptotes (horizontal and vertical if any), (d) intervals of increase and decrease, (e) local maximum and minimum values, (f) interval of concavity, (g) point of inflection, and (h) sketch the curve)

(a)

(b)

5. (20%) Find the volume of the solid generated by revolving the region bounded by and the lines y = 2 and x = 0 about(a) the line y = 2,(b) the line x = 4.

6. (20%) Find the first four nonzero terms in the Maclaurin series for(a)，and (b) sin^-1x = dt.

109年 - 109 國立臺北大學_轉學生招生考試試題_通訊工程學系二年級：微積分#117924

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