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`