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**Does lim x →0 sin 1/x exist? also...**

## Homework Statement

does lim x →0 sin(1/x) exist?

## The Attempt at a Solution

I am very new to calculus. From what i have understood till now, limit of a function at a point exists only if the left and right hand limits are equal. What would the graph of sin(1/x) look like? Would the left and right hand limits exist? Do they exist in all cases, for all functions?