Mathematics

Problem

The piecewise function

p

is defined as

p(x)=\begin{cases} px+3,& x<2\\ x^{2}-p^{2},& x\ge 2 \end{cases}

For which real value(s) of

p

does

\displaystyle\lim_{x\to 2}p(x)

exist? a)

p=1

b) both

-1+\sqrt{2}

and

-1-\sqrt{2}

p=-1+\sqrt{2}

only d)

\dfrac{1}{3}