Question

Evaluate the limit as x turns to 3

Lim √(x+1) - 2 / x-3

Answer 1

$\lim_{x\to3} \frac{\sqrt{x+1}-2}{x-3}\\ =\frac{0}{0}\\ \text{Therefore using l'hopital's rule we differentiate the numerator and denominator}\\ \lim_{x\to 3}(\frac{1}{2}(x+1)^{-\frac{1}{2}}=\frac{1}{4}$