Mathematics

Problem

A piecewise function

p

is defined by

p(x)=\begin{cases} 3x, & x<5,\\ 2x+1, & x>5. \end{cases}

Which statement best explains why

\displaystyle \lim_{x\to 5} p(x)

does not exist? a) The function is not defined at

x=5

, so no limit can be taken. b) The expressions on either side of

x=5

are linear, but have different slopes. c) The one-sided limits approach different finite values at

x=5

. d) Each one-sided limit is infinite, preventing a finite limit from existing.