True or False: Continuity on a closed interval is a sufficient condition for the differentiability of a function on that interval.

  True or False: If a function exhibits a jump discontinuity at a point within a closed interval, it is continuous on that interval.

  True or False: A function can be continuous on a closed interval if it has a vertical asymptote within that interval.

.   True or False: Continuity of a function on an open interval (a, b) guarantees continuity at the endpoints a and b.

.   True or False: If a function has a removable discontinuity at an endpoint of a closed interval, it is still considered continuous on that interval.

.   True or False: A function can be continuous on a closed interval even if it has a removable discontinuity within that interval.

  True or False: A piecewise-defined function can be continuous on a closed interval if each piece is continuous and their values match at the points of intersection.

.   True or False: A function can be continuous on a closed interval even if it exhibits an infinite oscillation at certain points within the interval.

.   True or False: If a function is continuous on a closed interval, it must have a horizontal asymptote within that interval.

.   True or False: A function needs to be defined at the endpoints of a closed interval to be considered continuous on that interval.