How do you determine the limit without substitution. ie. lim x--> -2 sqr(x-2)

Answer 1

lim sqrt(x-2) as x>-2?

there is no issue here, the limit is sqrt(-4) or 2i

Did I misunderstand your question?

Answer 2

But you can't find the square root of negative 4. I need to use another alternative besides substituting

Answer 3

I don't see the issue here.

answer 2 sqrt(-1)=2i

If you wanted to use an infinite series for sqrt, you could use a binomial expansion for (x+a)^k but I wouldn't want to spend weeks on it.