# Evaluate the following limit : lim(x→0)(√(a^2+x^2) - a)/x^2

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Evaluate the following limit : $\lim\limits_{\text x \to 0}\cfrac{\sqrt{a^2+\text x^2}-a}{\text x^2}$

lim(x→0)(√(a2+x2) - a)/x2

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Given $\lim\limits_{\text x \to 0}\cfrac{\sqrt{a^2+\text x^2}-a}{\text x^2}$

To find: the limit of the given equation when x tends to 0

Substituting x as 0, we get an indeterminant form of $\cfrac00$

Rationalizing the given equation

Formula: (a + b) (a - b) = a2 - b2

Now we can see that the indeterminant form is removed, so substituting x as 0

We get, $\lim\limits_{\text x \to 0}\cfrac{\sqrt{a^2+\text x^2}-a}{\text x^2}$ = $\cfrac1{a+a}=\cfrac1{2a}$