can anyone help with solving one-sided limits?

Question

anonymous · Answer

maybe

anonymous · Answer

i think i can

anonymous · Answer

find the indicated one-sided limit, if it exists: lim x --> 2 (from the left side) of (x-3)/(x+2)

anonymous · Answer

the answer is -1/4, just try the limit value and there you can see that the limit exist

anonymous · Answer

okay i think it makes sense now....so you can plug the number in so long as it is defined in the function?

anonymous · Answer

No, the function has to be continuous at that point. For example, consider$$f(x) = \begin{cases}0 & x \neq 0 \ 1 & x = 0\end{cases}.$$In this case $$\lim_{x \to 0}\ f(x) = 0,$$but$$f(0) = 1.$$This happens because the function is not continuous at 0. All polynomials, rational functions, exponentials, trigonometric functions and their inverses are continuous (at the points they are defined, obviously), so in that case you can just plug the number in.