課程名稱︰微積分甲上
課程性質︰大一必修
課程教師︰容志輝
開課學院：工學院
開課系所︰電機系、材料系
考試日期（年月日）︰2014/11/3
考試時限（分鐘）：50分鐘
試題 :
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103-1 Calculus class-2 2nd test
1. (a)
1 1
lim ( ─ - ──── )
x→0 x e^x - 1
(b)
x^2 sin( 1 / x )
lim ─────────
x→0 sin x
(c)
arcsin x ( 1 / x ^ 2 )
lim ( (─────) )
x→0 x
2. (a)
d -1
Find ─[ tanh ( sin x ) ]
dx
(b)
d x 3 4 1 + tanh x
Find ─[ x arccos (x) √( ────── ) ]
dx 1 - tanh x
╴ ╴
3. the following picture is right triangle with AB + AC = a. What is the
x maximizing the area of the triangle?
A
╱︳
a-x ╱ ︳x
╱ ︳
╱ ︳
B￣￣￣￣C
4. (1/x)
let f(x) = ( x + 2 ) e
(a) What is the domain of f(x)?
(b) Does f(x) have any vertical or horizontal asymptote?
(c) Calculate lim ( f(x) - x ) and find the slant asymptote of f(x).
x→±∞
(d) Find the interval of increase or decrease
(e) Find the interval of concavity and inflection points.
(f) Find the local maximum and minimum values.
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