数学分析考试试题.pdf
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A
120
f (x )
1
lim (n sin )
n →∞ n
lim n a n +b n (a 0, b 0)
n →∞
1 1 1
lim ( ... )
+ + +
n →∞ 1 1 2 1 2 3 n
+ + + ++
1−cos 1−cos 2x
lim
x
x →o sin x ⋅(e −1)
1 1
lim( 2 − 2 )
x →0 x sin x
2
x
−
2
cos x − e
lim
4
x →0 x
f (x) (ex +ln x) arcsin x
y f (ex )2f (x ) , f (x)
xy + + , d 2 y
e x y e 2
dx
⎧ 2 sin ,
x t t
⎨ 2
cos ;
y t t
⎩
d 2 y
y f (arctan x ) f (x ) 2
dx
lim ( x 2 −x +1 +ax +b) 0
x →+∞
1
2
y x 3
y ax3 +bx2
y (x −1)3 x 2
a 3 b3 3
( )
a 0,b 0 ∀x ∈(0,1), 2 + 2 ≥ a +b
x ( )
1−x
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