Let . Which statement best describes the behavior that prevents from existing as a…

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

Problem

Let

h(x)=\dfrac{1}{(x-2)^2}

. Which statement best describes the behavior that prevents

\displaystyle \lim_{x\to 2}h(x)

from existing as a finite number? (a) The function approaches different finite values from the left and right of

x=2

. (b) The function grows without bound on both sides of

x=2

, so the limit is infinite rather than finite. (c) The function oscillates between positive and negative values near

x=2

, preventing it from settling at any single value. (d) There is a single removable hole at

x=2

, so the limit is undefined only because the point is missing.