Question

Find the indicated limit, if it exists.

limit of f of x as x approaches 8 where f of x equals x plus 10 when x is less than 8 and f of x equals 10 minus x when x is greater than or equal to 8

8
18
The limit does not exist.
2

Answer 1

@Directrix

Answer 2

\[\lim_{x\rightarrow 8}f(x) = \lim_{x\rightarrow 8^-}f(x)=\lim_{x\rightarrow 8^+}f(x)\] in order to exists

Answer 3

But \(\lim_{x\rightarrow 8^-}f(x) = \lim_{x\rightarrow 8^-}(x+10) = 18\), and
\(\lim_{x\rightarrow 8^+}f(x) =\lim_{x\rightarrow 8^+}(10-x) = 2 \), you can see that these two limits are not equal, so... the limit does not exist.