$\begin{aligned} & \lim _{x \rightarrow \infty}\left(1+\frac{1}{a+b x}\right)^{c+c a x}=\lim _{x \rightarrow \infty}\left\{\left(1+\frac{1}{a+b x}\right)^{a+b x}\right\}^{\frac{c+c x}{a+b x}}=e^{d / b} \\ & \left\{\because \lim _{x \rightarrow \infty}\left(1+\frac{1}{a+b x}\right)^{a+b x}=e \text { and }\right. \left.\lim _{x \rightarrow \infty} \frac{c+d x}{a+b x}=\frac{d}{b}\right\} .\end{aligned}$