Chapter 3 - Derivatives - 3.5 Derivatives of Trigonometric Functions - 3.5 Exercises - Page 169: 1

=1

\[\begin{gathered} Evaluate\mathop {\,\,\lim }\limits_{x \to 0} \,\,\,\frac{{\sin \,x}}{x} \hfill \\ \hfill \\ \,set\,\,\,x = 0 \hfill \\ \hfill \\ then \hfill \\ \hfill \\ \sin \,\left( 0 \right) = 0 \hfill \\ x = 0 \hfill \\ \hfill \\ \mathop {\lim }\limits_{x \to 0} \,\,\frac{{\sin x}}{x} = \frac{0}{0} \hfill \\ \hfill \\ indeterminate\,\,\,form \hfill \\ from\,\,the\,\,theorem\,\,7.11 \hfill \\ \hfill \\ \mathop {\lim }\limits_{x \to 0} \,\,\frac{{\sin x}}{x} = 1 \hfill \\ \end{gathered} \]