求极限。。。。
答案:1 悬赏:70
解决时间 2021-01-25 10:42
- 提问者网友：焚苦与心
- 2021-01-25 00:43
求极限。。。。
最佳答案
- 二级知识专家网友：千杯敬自由
- 2021-01-25 01:22
(1)
y=π-x
lim(x->π) sinx/(π-x)
=lim(y->0) siny/y
=1
(2)
y= 1/2^n
lim(n->∞) 2^n. sin(a/2^n)
=lim(y->0) sin(ay) /y
=a
(3)
lim(x->0) (1-cos2x)/(xsinx)
=lim(x->0) 2(sinx)^2/(xsinx)
=lim(x->0) 2sinx/x
=2
(4)
lim(x->0) (x+2sinx)/(x+sinx)
lim(x->0) (x+2x)/(x+x)
=3/2
(5)
let
1/y = k/x
lim(x->∞) (1+ k/x)^x
=lim(y->∞) (1+ 1/y)^(ky)
=e^k
y=π-x
lim(x->π) sinx/(π-x)
=lim(y->0) siny/y
=1
(2)
y= 1/2^n
lim(n->∞) 2^n. sin(a/2^n)
=lim(y->0) sin(ay) /y
=a
(3)
lim(x->0) (1-cos2x)/(xsinx)
=lim(x->0) 2(sinx)^2/(xsinx)
=lim(x->0) 2sinx/x
=2
(4)
lim(x->0) (x+2sinx)/(x+sinx)
lim(x->0) (x+2x)/(x+x)
=3/2
(5)
let
1/y = k/x
lim(x->∞) (1+ k/x)^x
=lim(y->∞) (1+ 1/y)^(ky)
=e^k
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