Consider . On the standard window , , the graph appears to lie almost on the -axis…

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

Problem

Consider

p(x)=x^{2}\sin(100x)

. On the standard window

-10\le x\le 10

-10\le y\le 10

, the graph appears to lie almost on the

x

-axis near

x=0

. A tighter window of

-0.1\le x\le 0.1

-0.02\le y\le 0.02

reveals rapid oscillations whose amplitude shrinks toward

0

. What is

\displaystyle\lim_{x\to 0}p(x)

? (a)

1

(b) The limit does not exist because the function oscillates infinitely often. (c)

0

(d)

0.02