Chapter 2: Limits and Continuity - Practice Exercises - Page 101: 45

$$1$$

\begin{align*} \lim _{x \rightarrow \infty} \frac{x+\sin x+2 \sqrt{x}}{x+\sin x}&=\lim _{x \rightarrow \infty} \frac{1+\frac{\sin x}{x}+\frac{2}{\sqrt{x}}}{1+\frac{\sin x}{x}}\\ &=\frac{1+0+0}{1+0}\\ &=1 \end{align*}