AP

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

h(x)=x\sin\left(\frac{1}{x^2}\right)

. (a) Establish inequalities that bound

|h(x)|

for all sufficiently large

x>0

. (b) Using the bounds obtained in part (a), determine

\lim_{x\to\infty}h(x)

. (c) Comment briefly on how the behaviour of

\frac{1}{x^2}

x\to\infty

influences the limit obtained.