Question

${lim}_{x\to 3}\frac{x-3}{|x-3|},$ is equal to

• A. 1
• B. -1
• C. 0
• D. does not exist

Answer 1

The correct option is D

does not exist

${lim}_{x\to 3}\frac{x-3}{|x-3|}$
$LHLatx=3:$
${lim}_{x\to 3^{-}}\frac{x-3}{-(x-3)}\Rightarrow -1$
$RHLatx=3:$
${lim}_{x\to 3^{+}}\frac{x-3}{x-3}=1$
$LHL\ne RHL$