Evaluate the following limit : lim(x→a) (sin √x - sin √a)/(x - a)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to a}\cfrac{sin\sqrt {\text x}-sin \sqrt a}{\text x-a} \)

lim(x→a) (sin √x - sin √a)/(x - a)

Answer 1

we have \(\lim\limits_{\text x \to a}\cfrac{sin\sqrt {\text x}-sin \sqrt a}{\text x-a} \)