Question

Let $f : R \to 0, \infty$ be such that $\displaystyle\lim_{x\to5} f\left(x\right)$ exists and $\displaystyle\lim_{x\to5} \frac{\left(f\left(x\right)\right)^{2}-9}{\sqrt{\left|x-5\right|}} = 0$
Then $\displaystyle\lim_{x\to5} f\left(x\right)$ equals :

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (D)

$\ell im_{x\to5} \frac{\left(f\left(x\right)^{2}\right)-9}{\sqrt{\left|x-5\right|}} = 0$
$\ell im_{x\to 5} \left[\left(f\left(x\right)\right)^{2}-9\right] = 0$
$\ell im_{x\to 5} f\left(x\right) = 3$