lim _{x rightarrow 0} frac{sqrt{x^2+100}-10}{ | vedclass

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(C) To evaluate the limit $\lim _{x \rightarrow 0} \frac{\sqrt{x^2+100}-10}{x^2}$,we rationalize the numerator:$\lim _{x \rightarrow 0} \frac{\sqrt{x^

Vedclass · Accepted Answer

$0.05$

Vedclass · Answer

(C) To evaluate the limit $\lim _{x ightarrow 0} \frac{\sqrt{x^2+100}-10}{x^2}$,we rationalize the numerator:$\lim _{x ightarrow 0} \frac{\sqrt{x^2+100}-10}{x^2} 	imes \frac{\sqrt{x^2+100}+10}{\sqrt{x^2+100}+10}$$= \lim _{x ightarrow 0} \frac{(x^2+100)-100}{x^2(\sqrt{x^2+100}+10)}$$= \lim _{x ightarrow 0} \frac{x^2}{x^2(\sqrt{x^2+100}+10)}$$= \lim _{x ightarrow 0} \frac{1}{\sqrt{x^2+100}+10}$Substituting $x = 0$:$= \frac{1}{\sqrt{0+100}+10} = \frac{1}{10+10} = \frac{1}{20} = 0.05$Thus,the correct option is $C$.

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

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