\( \lim _{x \rightarrow 2^{-}} f(x)=5 \) and \( \lim _{x \rightarrow 2^{+}} f(x)=-5 \) then \( \lim _{x \rightarrow 2} f(x) \) does not exist. True False

True! Since the left-hand limit as \( x \) approaches 2 is 5 and the right-hand limit is -5, these two values do not match. For a limit to exist at a point, both one-sided limits must be equal. In this case, they are not, so \( \lim _{x \rightarrow 2} f(x) \) does indeed not exist. Understanding limits can be vital, especially in calculus. They set the groundwork for continuity and differentiability, which are key concepts in understanding more complex mathematical ideas. When limits do not exist, it often signals points of discontinuity, something to be aware of as you study functions!