$\underset{x→5}{\lim}\frac{x-5}{|x-5|}$ equals
Answer & explanation
Correct answer: option 4
$\underset{x→5^+}{\lim}\frac{x-5}{|x-5|}=\underset{x→5^+}{\lim}1=1$,
because for values to the right of 5, x – 5 > 0 ⇒ |x - 5| = (x – 5).
$\underset{x→5^-}{\lim}\frac{x-5}{|x-5|}=\underset{x→5^-}{\lim}-1=-1$
because for values to the left of 5, x – 5 > 0 ⇒ |x - 5| = -(x – 5).
$⇒\underset{x→5}{\lim}\frac{x-5}{|x-5|}$ doesn’t exist
Hence (D) is the correct answer.