Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Exercises - Page 73: 45

$$\lim _{x \rightarrow 0}(2 a+x)=2a $$

Given $$ \lim _{x \rightarrow 0}(2 a+x), \ \ \ a \ \ \text{is constant}$$ let $$ f(x) = 2a +x $$ Since, we have $$ f( 0)= 2a+0=2a $$ So, we get \begin{aligned} L&= \lim _{x \rightarrow 0}(2 a+x)\\ &= 2 a+0\\ &=2a \end{aligned}