Give an example to show that $\displaystyle \lim_{x \to 0}\frac{g(ax)}{x}$ need not exist if a=0.
Give an example to show that $\displaystyle \lim_{x \to 0}\frac{g(ax)}{x}$ need not exist if a=0.
What if $\displaystyle g(0)=c\ne0$?