Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Exercises - Page 73: 46

$$\lim _{h \rightarrow -2} (4a\ h +7 a)=-a $$

Given $$\lim _{h \rightarrow -2} (4a\ h +7 a), \ \ \ a \ \ \text{is constant}$$ let $$ f(h) = (4a\ h +7 a)$$ Since, we have $$ f(-2)= (-8 a+7 a)=-a $$ So, we get \begin{aligned} L&=\lim _{h \rightarrow -2} (4a\ h +7 a)\\ &= (-8a\ +7 a)\\ &= -a \end{aligned}