How do you evaluate the limit #sqrt(x-2)# as x approaches #-2#?

1 Answer
Jim H
Oct 17, 2016

It depends on the setting in which you are working.

Explanation:

If we intend to stay in the system of real numbers, then the limit does not exist because the is no open interval containing #-2# in the domain of #sqrt(x-2)#.
(The domain in the real number system is #[2,oo)#.)

If we are working in the set of complex numbers, then by continuity, #lim_(xrarr-2)sqrt(x-2) = sqrt(-4) = 2i#

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