Question

求帮忙解题，拜托了，无穷小，怎么解？

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Answer 1

方法如下，
请作参考：

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Answer 2

(10)
|cosn^2|≤1
lim(n->无穷 1/n=0
=>
lim(n->无穷 cosn^2/n =0
(11)
lim(x->0) ln(1+2x^2)/sin(x^2)
=lim(x->0) 2x^2/(x^2)
=2
(12)
lim(x->0) [1-e^(3x)]/tan(3x)
=lim(x->0) -(3x)/(3x)
=-1
(13)
lim(x->0-) [ 1- e^(1/x)]/[ 1+e^(1/x)]
=(1-0)/(1+0)
=1
(14)
lim(x->0) [(1+x)^5 -1]/(e^x -1)
=lim(x->0) [(1+x)^5 -1]/ x

=lim(x->0) 5x/ x
=5
(9)
|arctanx|≤π/2
lim(x->无穷) 1/x =0
=>
lim(x->无穷) arctanx/x =0