Question

$\underset{x\to 0}{lim}\frac{x}{|x|+x^2}$ is equal to.

• A. $1$
• B. $-1$
• C. $0$
• D. Does not exist

Answer 1

Answer: (D)

Does not exist

$\underset{x\to 0^{+}}{lim}f\left(x\right)=\frac{x}{x+x^2}=\frac{1}{1+x}=1$

$\underset{x\to 0^{-}}{lim}f\left(x\right)=\frac{x}{-x+x^2}=\frac{1}{-1+x}=-1$

Left hand limit $\ne$ right hand limit

Limit does not exist.