Does lim x →0 sin 1/x exist? also..... 1. The problem statement, all variables and given/known data does lim x →0 sin(1/x) exist? 3. 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?