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

Answer 1

Emilia Aguilar

#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]}

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Answer 2

Charles Anctil

To find the limit of (x)(sin(1/x)) as x approaches infinity, we can use the squeeze theorem. By applying the squeeze theorem, we can establish that the limit is equal to zero.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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