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^-)(-6+x)/(x^4)=(-6+0)/((0^-)^4)\to\left\{(-)/(+)\right\}\to=-\infty\\\\\lim\limits_(x\to0^+)(-6+x)/(x^4)=(-6+0)/((0^+)^4)\to\left\{(-)/(+)\right\}\to=-\infty \end{array}\right\}\Rightarrow\lim\limits_(x\to0)(-6+x)/(x^4)=-\infty`