Calculus with Applications (10th Edition)

A limit at x=a exists if 1. both one sided limits exist AND 2. they are equal ------------ In exercise 6, both the limit from the left and the limit from the right exist, and they both equal 4. Therefore $\displaystyle \lim_{x\rightarrow 2}F(x)$ exists and equals 4. In exercise 9, the left sided limit exists and equals $-1,$ the right sided limit exists and equals $-\displaystyle \frac{1}{2}$, BUT, they are not equal, so $\displaystyle \lim_{x\rightarrow-2}f(x)$ does not exist .