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