Mathematics

Problem

(a) State the numerical bounds satisfied by

\sin \theta

for every real number

\theta

. (b) For

x>0

, use the result from part (a) to write two inequalities that contain the term

\dfrac{\sin 3x}{x}

. (c) Using the inequalities from part (b), find

\displaystyle \lim_{x \to \infty} \dfrac{\sin 3x}{x}