# How to prove limit as x approaches 0 of x sin(1/x)= 0 ?

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Here's an answer using the squeeze or sandwich theorem.

We know that any sine must be between -1 or 1, or in mathematical terms,

If

Multiplying both sides by

And since

We can use the squeeze theorem to say

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Here we are, one year later with a different way to solve this in case somebody comes across this:

If we say

Remember that the sine is always a number between -1 and 1, so when

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