Question

求解数学题极限！！在线等急！

Answer 1

如下

Answer 2

追问

我重新发给你几个题帮我做，我给你200采纳

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追答

可以的

Answer 3

(1)
let
y=1/x
lim(x->∞) 3xsin(1/x)
=3lim(y->0) siny /y
=3
(2)
y=1/x
lim(x->∞) [(x^2+1)/(x+3) ]. sin(1/x)
=lim(y->0) [( (1/y)^2+1)/(1/y+3) ]. siny
=lim(y->0)[ (y^2+1)/(y+3)] . lim(x->0) (siny/y)
=lim(y->0)[ (y^2+1)/(y+3)]
=1/3
(3)
lim(x->0) |x|/(2x)
lim(x->0+) |x|/(2x) = 1/2
lim(x->0-) |x|/(2x) = -1/2
=>lim(x->0) |x|/(2x) 不存在
(4)
lim(x->0) [√(1-2x) -1 ]/(3x)
=lim(x->0) [(1-2x) -1 ]/{ (3x).[√(1-2x) +1 ] }
=lim(x->0) -2x/{ (3x).[√(1-2x) +1 ] }
=(1/2) lim(x->0) -2x/(3x)
= -1/3
(5)
lim(x->∞) x^2.[ 1/(x+1) -1/(x-2) ]
=lim(x->∞) x^2. { -3/[(x+1)(x-2) ] }
=lim(x->∞) { -3/[(1+1/x)(1-2/x) ] }
=-3

追问

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