Explain why the function f(x)= cases x^2,&x 2 5,&x=2 cases is discontinuous at even…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Explain why the function

f(x)=\begin{cases}x^2,&x\neq 2\\5,&x=2\end{cases}

is discontinuous at

x=2

even though

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

exists.