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研究所、轉學考(插大)-微積分
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108年 - 108 國立臺灣大學轉學生招生考試試題_(商、管、農、經學院聯招) ：微積分(C)#113211
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1 Lemniscate (x
2
+ y
2
)
2
= x
2
-y
2
At the point (x,y)=
dy/dx=?
其他申論題
(a) Find the limit: (6分)
#483668
(b) Let a and b be constants with0 ＜ a ＜ b. Does the sequence {(an +bn)1/n} converges? If it does converge, what is the limit? (6 分)
#483669
(a) A number a is called a fixed point of a function f if f(a) = a. Prove that if f'(x)≠1 for all real numbers x, then f has at most one fied point. (6 分)
#483670
(b) Show that if converges，thenconverges.(6分)
#483671
2. If x3+y3= 3xy, then x + y≤max = ?
#483673
3. The probability density function of an exponential distribution is f(x) = if x ≧ 0, f(x) = 0 if x ＜ 0. Find the expected value E(x) = ?
#483674
4.f(x) = = ?
#483675
5. f(x) = 1/(x2 - x-2) = Taylor series ==?
#483676
6.A =(-1,0), B=(0,1),C =(2,2). Use the method of least squares to find a line y = mx+b that best fits A, B, C. m =?, b=?.
#483677
7. = ?
#483678
dy/dx=?
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dy/dx=?