Barrons AP Calculus - David Bock

FIGURE N2–10

EXAMPLE 29
Is (x ≠ 2) 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.