How do you find the limit as x approaches 2 of the piecewise function f(x)={(4-x^2,if x<=2),(x-1,if x>2):} ?

1 Answer
Sep 7, 2014

Since the left-hand limit and the right-hand limit at x=2 do not match, the limit lim_{x to 2}f(x) does not exist.

Let us find the left-hand limit.
lim_{x to 2^-}f(x)=lim_{x to 2^-}(4-x^2)=4-(2)^2=0

Let us find the right-hand limit.
lim_{x to 2^+}f(x)=lim_{x to 2^+}(x-1)=(2)-1=1

Since the above one-sided limits at x=2 do not match, the limit at x=2 does not exist.