Question

高等数学题，有会的吗？过来帮帮忙

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Answer 1

(1)
y=x-π
lim(x->π) sinx/(x-π)
=lim(y->0) -siny/y
=-1
ans : A
(2)
ans :B
lim(x->∞) (1+ 1/x)^(2x) = e^2
(3)
(x-1)/(x+1) =1- 2/(x+1)
let
1/y = 2/(x+1)
lim(x->∞) [(x-1)/(x+1)]^(x+1)
=lim(x->∞) [1- 2/(x+1) ]^(x+1)
=lim(x->∞) [1- 2/(x+1) ]^x
=lim(y->∞) [1- 1/y ]^(2y)
=e^(-2)
ans :A
(4)
x/(1+x) = 1- 1/(1+x)
let
1/(1+x) =1/y
lim(x->∞) [x/(1+x)]^x
=lim(x->∞) [1 - 1/(1+x)]^x
=lim(y->∞) [1 - 1/y]^(y-1)
=lim(y->∞) [1 - 1/y]^y
=e^(-1)
ans : C
(5)
let
x/a =y
lim(x->0) ( 1+ x/a)^(b/x)
=lim(y->0) ( 1+ y)^(b/(ay))
=e^(b/a)
ans : D

追问

谢谢，全正确了