Question
Given an $\varepsilon-\delta$ proof of the fact that$$\lim _{x \rightarrow 0} 2 x \sin \left(\frac{1}{x}\right)=0$$
Step 1
Step 1: We want to show that for any given $\varepsilon > 0$, there exists a $\delta > 0$ such that if $0 < |x - 0| < \delta$, then $|2x\sin(\frac{1}{x}) - 0| < \varepsilon$. Show more…
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