The function is defined by

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

Problem

The function

h

is defined by

h(x)=\dfrac{x+1}{(x-2)^3}

. Which statement best explains the value of

\displaystyle \lim_{x\to2^+}h(x)

? (a) Because the denominator has higher degree than the numerator, the fraction approaches

0

, so the limit is

0

. (b) Since

x+1

is positive and

(x-2)^3

approaches

0

through positive values, the quotient grows without bound in the positive direction, so the limit is

\infty

. (c) Since

x+1

is positive and

(x-2)^3

approaches

0

through negative values, the quotient grows without bound in the negative direction, so the limit is

-\infty

. (d) Because both numerator and denominator approach

0

, the limit is indeterminate and therefore does not exist.