Limits question bank (Mathematics)

If $\lim _{x \rightarrow 0} \frac{\left(e^{k x}-1\right) \sin k x}{x^{2}}=4$, then $k$ is equal to

Given $f(x)=\frac{a x+b}{x+1}, \lim _{x \rightarrow \infty} f(x)=1 \quad$ and $\lim _{x \rightarrow 0} f(x)=2$, then $f(-2)$ is