MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
A function g is graphed so that as x→2, both one-sided limits equal 5. The point (2,5) is an open circle, and a closed dot is shown at (2,1). Which statement best describes g at x=2?
(a) g is continuous at x=2 because g(2) is defined.
(b) g is discontinuous at x=2 because there is a jump discontinuity.
(c) g is discontinuous at x=2 because the discontinuity is removable.
(d) g is continuous at x=2 because the limit exists.