极限题,求急呀
1个回答
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(1)
let y=π-x
lim(x->π) sinx/(π-x)
=lim(y->0) siny /y
=1
(2)
(x+a)/(x-a) = 1- 2a/(x-a)
let
1/y = 2a/(x-a)
lim(x->∞) [(x+a)/(x-a)]^x
=lim(x->∞) [ 1- 2a/(x-a)]^x
=lim(y->∞) (1- 1/y)^(2ay +a)
=lim(y->∞) (1- 1/y)^(2ay)
=e^(-2a)
(3)
|cosx| ≤1
lim(x->∞) e^x/(e^(2x) +1) =0
---------------
lim(x->∞) cosx/(e^x +e^(-x))
=lim(x->∞) [e^x/(e^(2x) +1) ].cosx
=0
let y=π-x
lim(x->π) sinx/(π-x)
=lim(y->0) siny /y
=1
(2)
(x+a)/(x-a) = 1- 2a/(x-a)
let
1/y = 2a/(x-a)
lim(x->∞) [(x+a)/(x-a)]^x
=lim(x->∞) [ 1- 2a/(x-a)]^x
=lim(y->∞) (1- 1/y)^(2ay +a)
=lim(y->∞) (1- 1/y)^(2ay)
=e^(-2a)
(3)
|cosx| ≤1
lim(x->∞) e^x/(e^(2x) +1) =0
---------------
lim(x->∞) cosx/(e^x +e^(-x))
=lim(x->∞) [e^x/(e^(2x) +1) ].cosx
=0
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