Question

If (x) = |x - 2|, then

(A) lim(x →2+)f(x) ≠ 0

(B) lim(x →2-) f(x) ≠ 0

(C) lim(x →2+) f(x) ≠ lim(x →2-)f(x)

(D) f(x) is continuous at x = 2

Answer 1

Answer is (D) f(x) is continuous at x = 2

Here f(2) = 0

lim(x →2-) f(x) = lim(h →0) f(2 - h) = lim(h →0) |2 - h - 2| = 0

lim(x →2+) f(x) = lim(h →0)f(2 + h) = lim(h →0) |2 + h - 2| = 0

Hence, it is continuous at x = 2.