## Calculus (3rd Edition)

$$\lim _{t \rightarrow 0+} \sqrt{t} \cos \left(\frac{1}{t}\right)=0$$
Since for $t>0$ $$-1 \leq \cos \left(\frac{1}{t}\right) \leq 1$$ Then $$-\sqrt{t} \leq \sqrt{t} \cos \left(\frac{1}{t}\right) \leq \sqrt{t}$$ and $$\lim _{t \rightarrow 0+}-\sqrt{t}=\lim _{t \rightarrow 0+} \sqrt{t}=0$$ Hence, by the Squeeze Theorem, we get $$\lim _{t \rightarrow 0+} \sqrt{t} \cos \left(\frac{1}{t}\right)=0$$