Mathematics

Mathematics

Problem

The function q(x)=sin⁡ ⁣(1x)q(x)=\sin\!\left(\dfrac{1}{x}\right) is graphed on −1≤x≤1-1\le x\le1, but the resulting picture near x=0x=0 is too dense to judge the limit. Specify a narrower symmetric xx-interval that would better reveal the local behavior, and state in one sentence how that view would help decide whether lim⁡x→0q(x)\displaystyle \lim_{x\to0}q(x) exists.

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