Q.Evaluate : $\lim_{x \to \infty} x \tan\left(\dfrac{1}{x}\right)$.

Limits of sums, differences, constant multiples, products, and quotients (with a non-zero denominator limit) can be built from the limits of the individual pieces. Alongside these rules, a short list of standard limits is used as known results: $\lim_{x\to0}\frac{\sin x}{x}=1$, $\lim_{x\to\infty}\left(1+\frac1x\right)^x=e$, $\lim_{x\to0}\frac{e^x-1}{x}=1$, and $\lim_{x\to0}\frac{\log(1+x)}{x}=1$. A c …