Question

Use the information given in the first image to evaluate the limit.

Answer 1

Given:-

$\lim _{x\rightarrow2}h(x)=5,\lim _{x\rightarrow2}g(x)=0$

To find:-

$\lim _{x\rightarrow2}\lbrack g(x)+h(x)\rbrack$

Now we use the formula,

$\lim _{x\rightarrow a}\lbrack g(x)+h(x)\rbrack=\lim _{x\rightarrow a}g(x)+\lim _{x\rightarrow a}h(x)$

So we get,

$\begin{gathered} \lim _{x\rightarrow a}\lbrack g(x)+h(x)\rbrack=\lim _{x\rightarrow a}g(x)+\lim _{x\rightarrow a}h(x) \\ \text{ =5+0} \\ \text{ =5} \end{gathered}$

So the required solution is,

$\lim _{x\rightarrow2}\lbrack g(x)+h(x)\rbrack=5$