Discussion Forum



1)

$\lim_{x \rightarrow 0}\frac{\sqrt{x^{2}+100}-10}{x^{2}}=$


A) 0

B) 0.1

C) 0.05

D) -0.05

Answer:

Option C

Explanation:

$\lim_{x \rightarrow 0}\frac{\sqrt{x^{2}+100}-10}{x^{2}}$

   =$\lim_{x \rightarrow 0}\frac{(\sqrt{x^{2}+100}-10)(\sqrt{x^{2}+100}+10)}{x^{2}(\sqrt{x^{2}+100}+10)}$

   =$\lim_{x \rightarrow 0}\frac{x^{2}+100-100}{x^{2}(\sqrt{x^{2}+100}+10)}$

   =  $\lim_{x \rightarrow 0}\frac{1}{\sqrt{x^{2}+100}+10}$

  = $\frac{1}{10+10}= \frac{1}{20}=0.05$

 Hence, option (c) is correct