limits - How to answer the question from Calculus by Michael Spivak Chapter 5 Problem 14

1. Prove that if $\lim\limits_{x\rightarrow0}{\frac{f(x)}x}=l$ and $b\neq 0$, then $\lim\limits_{x\rightarrow0}{\frac{f(bx)}x}=bl$. Hint: Write $\frac{f(bx)}x=b\frac{f(bx)}{bx}$


2. What happens if $b=0$?


3. Part 1 enables us to find $\lim\limits_{x\rightarrow0}{\frac{\sin{2x}}{x}}$ in terms of $\lim\limits_{x\to0}\frac{\sin x}x$. Find this limit in another way.

This is a question from Calculus by Michael Spivak Chapter 5 Problem 14.