Question

Evaluate
$\rm \displaystyle \lim_{x\to 3}\ \frac{\sqrt{x^{2}+1}-\sqrt{10}}{x-3}$

Answer 1

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Answer 2

Answer:

$\frac{3}{10}$

Step-by-step explanation:

$\rm \displaystyle \lim_{x\to 3}\ \frac{\sqrt{x^{2}+1}-\sqrt{10}}{x-3}$

Apply directly  $\lim_{x\to 3}$

we get ,$\frac{\sqrt{10}-\sqrt{10}}{3-3}$ = $\frac{0}{0}$ form

So, apply L hospital rule (In this rule we differentiate the each term with respect to the variable ) we get,

$\lim_{x\to 3}\frac{x}{\sqrt{x^{2}+1 } }$

Now apply $\lim_{x\to 3}$ we get $\frac{3}{\sqrt{10} }$

So, the required answer of $\rm \displaystyle \lim_{x\to 3}\ \frac{\sqrt{x^{2}+1}-\sqrt{10}}{x-3}$ is $\frac{3}{\sqrt{10} }$