Question

$\underset{x\to 0^{-}}{lim}\left(\frac{5x+2|x|}{7x+3|x|}\right)$ is equal to

• A. $\frac{3}{4}$
• B. $\frac{7}{10}$
• C. $0$
• D. $\infty$

Answer 1

The correct option is A $\frac{3}{4}$

If $x\to 0^{-}$, then $|x|=-x(\because x<0)$
$\underset{x\to 0^{-}}{lim}\left(\frac{5x+2|x|}{7x+3|x|}\right)=\underset{x\to 0^{-}}{lim}\left(\frac{5x-2x}{7x-3x}\right)=\underset{x\to 0^{-}}{lim}\frac{3x}{4x}=\frac{3}{4}$