Evaluate lim(x→4) (3 - √(5 + x))/(1 - √(5 - x))

Question

Evaluate \(\lim\limits_{\text x \to4}\left(\cfrac{3-\sqrt{5+\text x}}{1-\sqrt{5-\text x}}\right) \)

lim(x→4) (3 - √(5 + x))/(1 - √(5 - x))

Answer 1

To evaluate \(\lim\limits_{\text x \to4}\left(\cfrac{3-\sqrt{5+\text x}}{1-\sqrt{5-\text x}}\right) \)

lim(x→4) (3 - √(5 + x))/(1 - √(5 - x))

Formula used: Multiplying numerator and denominator with conjugates of numerator and denominator i.e

Thus, the value of \(\lim\limits_{\text x \to4}\left(\cfrac{3-\sqrt{5+\text x}}{1-\sqrt{5-\text x}}\right) \)is \(-\cfrac13\)