How do you find the limit of $(x) (sin (\frac{1}{x}))$ $(x)(sin(1/x))$ as x approaches infinity?

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Answer 1 · 2017-01-10T17:19:46

$lim_(x->+oo) xsin(1/x) = 1$

Substitute $t=1/x$ .

Evidently we have:

$lim_(x->+oo) t(x) = 0$

Thus:

$lim_(x->+oo) xsin(1/x) = lim_(t->0) (sin t)/t =1$

graph{xsin(1/x) [-10, 10, -5, 5]}

How do you find the limit of (x)(sin(1/x)) (x)(sin(1x)) (x)(sin(1/x)) as x approaches infinity?