Question

Which of the following function(s) has/have removable discontinuity at x = 1?

(A) f(x) = 1/In|x|

(B) f(x) = (X² - 1)/(x³ - 1)

(C) f(x) = 2^{-2^(1/(1 - x))}

(D) f(x) = (√(x + 1) - √2x)/(x² - x)

Answer 1

Answer is (B), (D)

(A) lim_(x →1) f(x) does not exist

(B) lim_(x →1) f(x) = 2/3

Hence, f(x) has removable discontinuity at x = 1.

(C) lim_(x →1) f(x) does not exist

(D) lim_(x→1) f(x) = - 1/2√2

Hence, f(x) has removable discontinuity at x = 1.