Prove-using-the-squeeze-law-of-functions-that-lim-x-a-x-a-Recall-that-the-squeeze-theorem-states-that-if-f-x-g-x-h-x-and-lim-x-a-f-x-lim-x-a-h-x-L-then-lim-x-a

Question Number 122192 by physicstutes last updated on 14/Nov/20

Prove using the squeeze law of functions that

\lim_{x \to a} \sqrt{x} = \sqrt{a} .

Recall that the squeeze theorem states that if

f (x) ⩽ g (x) ⩽ h (x)

and \lim_{x - a} f (x) = \lim_{x \to a} h (x) = L

then, \lim_{x \to a} g (x) = L .