Given \(\lim\limits_{\text x \to 2}\cfrac{\sqrt{1+4\text x}-\sqrt{5+2\text x}}{\text x -2} \)
To find: the limit of the given equation when x tends to 2
Substituting x as 2, 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 2
We get \(\lim\limits_{\text x \to 2}\cfrac{\sqrt{1+4\text x}-\sqrt{5+2\text x}}{\text x -2} \) = \(\cfrac2{(3+3)}=\cfrac13\)