What is $lim x → ∞ cos(1/x)/(1+1/x)$ ?

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$lim x → ∞ cos(1/x)/(1+1/x)$

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Answer 1 · 2018-04-22T11:38:20

The limit of the required function would be 1.

First look at the limit of $cos(1/x)$ as $x-> oo$ :
as $x -> oo$ : $1/x -> 0$
Thus $cos(0)=1$

Then look at the limit of the bottom line:
$1+1/x -> 1+0$ as $x->oo$

Putting the numerator and denominator together we get:
$lim x-> oo 1/1=1$