So I was trying to do some problems from this website. And on Problem number 10 I tried to do the following:
$\lim_{x \to 0} \frac{x^3-7x}{x^3}$
Multiply everything by $\frac{x^{-3}}{x^{-3}}$
$\lim_{x \to 0} \frac{x^3-7x}{x^3}\times\frac{x^{-3}}{x^{-3}}$
Which I got equals:
$\lim_{x \to 0} \frac{1-7x^{-2}}{1}$
Plug in $0$ for $x$ and I get:
$\frac{1}{1} = 1$
But, the answer according to the website is $-\infty$. (And therefore no limit exists). What was wrong about multiply by $\frac{x^{-3}}{x^{-3}}$ ?