Chapter 2: Limits and Continuity - Additional and Advanced Exercises - Page 104: 28

$$1$$

\begin{align*} \lim _{x \rightarrow 0} \frac{\sin \left(x^{2}+x\right)}{x}&=\lim _{x \rightarrow 0} \frac{\sin \left(x^{2}+x\right)}{x^{2}+x} \cdot(x+1)\\ &=\lim _{x \rightarrow 0} \frac{\sin \left(x^{2}+x\right)}{x^{2}+x} \cdot \lim _{x \rightarrow 0}(x+1)\\ &=1 \cdot 1\\ &=1 \end{align*}