Mathematics

Problem

Let the function

f

be defined by

f(x)=\begin{cases} 5-2x, & x<1,\\ 3x-1, & x\ge 1. \end{cases}

Respond to each part, showing all necessary limit notation. a. Part 1: (a) Evaluate

\displaystyle \lim_{x\to1^-}f(x)

. b. Part 2: (b) Evaluate

\displaystyle \lim_{x\to1^+}f(x)

. c. Part 3: (c) Does

\displaystyle \lim_{x\to1}f(x)

exist? Provide a brief justification based on your results from parts (a) and (b).