Consider for then

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Consider

f(x) = \lim_{n \to \infty} \frac{x^{n+1} - \sin x^n}{x^n + \sin x^n}

for

x > 0, x \neq 1, f(1) = 0

then (1)

f

is continuous at

x = 1

(2)

f

has a finite discontinuity at

x = 1

(3)

f

has an infinite or oscillatory discontinuity at

x = 1

(4)

f

has a removal type of discontinuity at

x = 1