Given \(\lim\limits_{\text x \to a}\cfrac{\text x-a}{\sqrt{\text x}-\sqrt a}\)
To find: the limit of the given equation when x tends to a
Substituting x as 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 a
We get \(\lim\limits_{\text x \to a}\cfrac{\text x-a}{\sqrt{\text x}-\sqrt a}\) = \(\sqrt a+\sqrt a=2\sqrt a\)