Let g(x)= cases 3, & x<2 5, & x 2 cases Which statement best describes the…
MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
Let
g(x)={3,5,x<2x≥2
Which statement best describes the discontinuity of g at x=2?
(a) No discontinuity; g is continuous at x=2 because g(2) exists.
(b) Removable discontinuity, because redefining g(2) could make the limits match.
(c) Jump discontinuity, because the one-sided limits are finite but unequal.
(d) Infinite discontinuity, because the function "jumps" so the limit is unbounded near x=2.