Evaluate the following limit : lim(x→1) (√(3 + x) - √(5 - x))/(x^2 - 1)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to 1}\cfrac{\sqrt{3+\text x}-\sqrt{5-\text x}}{\text x^2-1} \)

lim(x→1) (√(3 + x) - √(5 - x))/(x² - 1)

Answer 1

Given \(\lim\limits_{\text x \to 1}\cfrac{\sqrt{3+\text x}-\sqrt{5-\text x}}{\text x^2-1} \)

To find: the limit of the given equation when x tends to 1

Substituting 1 as we get an indeterminant form of \(\cfrac00\)

Rationalizing the given equation

Now we can see that the indeterminant form is removed, so substituting x as 1

We get \(\lim\limits_{\text x \to 1}\cfrac{\sqrt{3+\text x}-\sqrt{5-\text x}}{\text x^2-1} \) = \(\cfrac{2}{2(2+2)}=\cfrac14\)