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

`\lim_(x\to8) \left\{\begin{array}{cc}x+10&x\ \textless \ 8\\10-x&x\geq8\end{array}\right\\\\ \lim_(x\to8^-) x+10=8+10=18\\ \lim_(x\to8^+) 10-x=10-8=2`


`\lim_(x\to8^-) \\ot =\lim_(x\to8^+) \Rightarrow` there is no two-sided limit