Question

Evaluate
$\rm \displaystyle \lim_{x\to 3}\ \frac{x^{2}+\sqrt{x+6}-12}{x^{2}-9}$

Answer 1

Solution :

Given

$\rm \displaystyle \lim_{x\to 3}\ \frac{x^{2}+\sqrt{x+6}-12}{x^{2}-9}$

= Lt [x²+√x+6-12]'/(x²-9)'

= Lt { 2x + 1/[2√x+6]}/2x

= { 2×3 + 1/[2√(3+6) }/( 2×3 )

= [ 6 + 1/6 ]/6

= ( 36 + 1 )/36

= 37/36

••••