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

Answer 1

$f(x)= \left \{ {{x + 10; \ \ \ x \ \textless \ 8} \atop {10-x; \ \ \ x \geq 8}} \right. \\ \\ lim_{x \rightarrow 8} (f(x))^-=8+10=18 \\ lim_{x \rightarrow 8} (f(x))^+=10-8=2 \\ Since \ lim_{x \rightarrow 8} (f(x))^- \neq lim_{x \rightarrow 8} (f(x))^+$
Therefore, the limit does not exist.