What is the limit of sqrt(4-x^2) as x approaches 2?

1 Answer
May 22, 2015

It is 0. (Edit: I am incorrect on this. The limit does not exist. The limit as x goes to 2 from the left, is 0.)

lim_(xrarr2) x^2 = 4, so

lim_(xrarr2) (4-x^2) = 4-4=0.

Therefore,

lim_(xrarr2) sqrt(4-x^2) = sqrt(4-4)=sqrt0 =0.
(Edit: my error is in this step. We cannot use one sided continuity to evaluate a two sided limit.)


The graph of sqrt(4-x^2):
graph{sqrt(4-x^2) [-10, 10, -5, 5]}

I stand corrected. The limit does not exist. (I overlooked the domain issue.)