Barrons AP Calculus

Figure  N2–10

Example 29 __

Is continuous at x = 2?

SOLUTION: Note that k(x) = x + 2 for all x ≠ 2. The function is continuous
everywhere except at x = 2, where k is not defined. The discontinuity at 2 is
removable. If we redefine f(2) to equal 4, the new function will be continuous
everywhere. See Figure N2–11.

Figure  N2–11

Example 30 __

Is continuous at x = 1?

SOLUTION: f(x) is not continuous at x = 1 since . This
function has a jump discontinuity at x = 1 (which cannot be removed). See
Figure N2–12.