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研究所、轉學考(插大)-微積分
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106年 - 106 國立清華大學碩士班考試入學試題_科技管理研究所/乙組:微積分#110853
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1. Find an equation of the tangent to the curve y
3
= xy + x + 1 at the point (0, 1).
其他申論題
(b) The Maclaurin series (the 'Taylor series at a = 0) for x is__(20)__.
#474793
1. Find the equation of the curve on thexy-plane that passes through (3,1) such that for any point P on the curve, the midpoint of the tangent line at P that lies in the first quadrant is P itself.
#474794
(e) Find.
#474795
(b) Assume that on another curve , f obtains local naximumn at (Jc0,yo) which is near . Use linear epproimation to estimate
#474796
2. Evaluate
#474798
3. A function f is defined by Find the maximum value of f.
#474799
4. Find the solution of the differential equation that satisfes the initial condition y (1) = 0.
#474800
5. If f is concave upward on [a,b], show that
#474801
6. If ao + a1 + a2 +...+ = 0, show that
#474802
7. Find the minimum distance from the origin in to the surface z = 6xy + 7.
#474803
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