Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises - Page 126: 64

$\lim\limits_{h \to 0}sin(a+h) = sin~a$

According to (6): $\lim\limits_{\theta \to 0}sin~\theta = 0$ $\lim\limits_{\theta \to 0}cos~\theta = 1$ We can evaluate $\lim\limits_{h \to 0}sin(a+h)$: $\lim\limits_{h \to 0}sin(a+h)$ $=\lim\limits_{h \to 0}~(sin~a~cos~h+cos~a~sin~h)$ $=[sin~a~(1)+cos~a~(0)]$ $= sin~a$