Question

Limit (4-x^2)/(3-under root x^2+5) at point 2

Answer 1

Answer:

The answer is 6

Step-by-step explanation:

Given limit

        $=\displaystyle \lim_{x\to 2}\dfrac{4-x^2}{3-\sqrt{x^2+5}}$

Rationalize the denominator

       $=\displaystyle \lim_{x\to 2}\dfrac{4-x^2}{3-\sqrt{x^2+5}}\times \dfrac{3+\sqrt{x^2+5}}{3+\sqrt{x^2+5}}\\\\=\displaystyle \lim_{x\to 2}\dfrac{4-x^2}{3^2-(x^2+5)}\times \dfrac{3+\sqrt{x^2+5}}{1}\\\\=\displaystyle \lim_{x\to 2}\dfrac{4-x^2}{4-x^2}\times \dfrac{3+\sqrt{x^2+5}}{1} \\\\=\displaystyle \lim_{x\to 2}\dfrac{3+\sqrt{x^2+5}}{1}=3+\sqrt{2^2+5}\\=3+3=6$