課程名稱︰微積分甲上
課程性質︰
課程教師︰曾琇瑱
開課學院：（非一二組）..生農嗎..？還是公衛
開課系所︰（非一二組）..生農嗎..？還是公衛
考試日期（年月日）︰98/11/06 五
考試時限（分鐘）：110 mins
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(5%) Find g(x) and h(x) such that f(x)=g(h(x)) where
5 ____
f(x)=_________+3√x+4
_____
√x+4
2.(9%) Find the follow limits
_
√x-1
(a) lim _______
x→1 x-1
∣x∣
(b)lim - _____
x→0- x
(c)lim 2e^(x-x^2)
x→+∞
3.(8%) Show that lim 1/x = 1
x→1
4.(5%) Make a rough sketch of the derivative of the given graph of f(x)
1 _____
5.(15%) Let f(x) = _______ + √x^2+x - x answer the follow problems
x^2-3x
(a) Find the domain of f(x)
(b) Find the asymptotes of f(x)
(c) Find f'(x)
6.(5%) Determine whether f(x) is continuous(give the proof) or discontinuous
(give your reason) at x=3 where f(x)=2x^2 -x if x<3 and f(x)=3-x if
x≧3
7.(18%) Find dy/dx of the follow function
(a) y= [(5x^2 +2)^3]coshlnx
_____
√1+e^x
(b) y=tan^-1 ____________
__________
√1+(sinx)^2
(c) 4cosxsiny=1
8.(10%) If f(x)+(x^2)[f(x)]^3 = 10 and f(1)=2 find f'(1)
9.(10%) Use the definition of derivation to prove that
ln(1+x)
lim _______ = 1
x→0 x
10.(15%)
(a) State the Intermediate Value Theorem
(b) Show that there is a root of the equation sinx=2x-(x^3-1)^-1
between -π/2 and π/2
(c) Suppose that f is continuous on the interval [1,5] and the only solution
of the equation f(x)=6 are x=1 and x=4 If f(2)=8 explain why f(3)>6
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※ tom5707:轉錄至看板 b982040XX 11/12 01:01