Mathematics

Problem

Evaluate the following limits, showing each step clearly. a. (i)

\displaystyle \lim_{x \to 0} \dfrac{\sin 7x}{x}

b. (ii) Using the value obtained in part (i), find

\displaystyle \lim_{h \to 0} \dfrac{\sin 7h}{5h}

c. (iii) Hence determine

\displaystyle \lim_{x \to 0} \dfrac{\sin 7x}{\tan 5x}