Sarthaks Test
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Evaluate the following limit : \(\lim\limits_{\text x \to 0}\cfrac{\sqrt{1+\text x+\text x^2}-1}{\text x} \)

lim(x→0)(√(1 + x + x2) - 1)/x

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Given \(\lim\limits_{\text x \to 0}\cfrac{\sqrt{1+\text x+\text x^2}-1}{\text x} \)

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, \(\lim\limits_{\text x \to 0}\cfrac{\sqrt{1+\text x+\text x^2}-1}{\text x} \) = \(\cfrac1{1+1}=\cfrac12\)

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