Question

Find the limit of the function algebraically lim x=0 -6+x/x^4

Answer 1

$\left\begin{array}{ccc}\lim\limits_{x\to0^-}\dfrac{-6+x}{x^4}=\dfrac{-6+0}{(0^-)^4}\to\left\{\dfrac{-}{+}\right\}\to=-\infty\\\\\lim\limits_{x\to0^+}\dfrac{-6+x}{x^4}=\dfrac{-6+0}{(0^+)^4}\to\left\{\dfrac{-}{+}\right\}\to=-\infty \end{array}\right\}\Rightarrow\lim\limits_{x\to0}\dfrac{-6+x}{x^4}=-\infty$