[See Steps] Use the \epsilon-δ definition to show that (a) lim _x \rightarrow 1(x^2+1)=2 ; \text (b) lim _x \rightarrow 0 x sin
Question: Use the \(\epsilon-\delta\) definition to show that
\[(a) \lim _{x \rightarrow 1}\left(x^{2}+1\right)=2 ; \quad \text { (b) } \lim _{x \rightarrow 0} x \sin \frac{1}{x}=0\]
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