Given \(\lim\limits_{\text x \to 1}\cfrac{\sqrt{5\text x-4}-\sqrt {\text x}}{\text x-1} \)
To find: the limit of the given equation when x tends to 1
Substituting x as 1, 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 1
We get \(\lim\limits_{\text x \to 1}\cfrac{\sqrt{5\text x-4}-\sqrt {\text x}}{\text x-1} \) = \(\cfrac4{1+1}\) = 2
