Mathematics

Problem

A function

P

is defined by

P(x)=\begin{cases} 5,& x\le3,\\ mx+2,& x>3, \end{cases}

where

m

is a real constant. a. (i) Find the left–hand and right–hand limits of

P(x)

x\to3

. b. (ii) Determine the value of

m

for which

P

is continuous at

x=3