Question

I have a calculus question about limit laws. Pic included.

Answer 1

Given:

`f(x)=\begin{cases}{√(-1-x)}+2\text{ }if\text{ }x<-2 \\ {2\text{ }} \\ {2x+7}\text{ }if\text{ }x>-2\end{cases}if\text{ }x=-2`

Required:

We have to find

`\lim_(x\to-2^-)f(x),\text{ }\lim_(x\to-2^+)f(x),\text{ and }\lim_(x\to-2)`

Step-by-step explanation:

`\lim_(x\to-2^-)f(x)=\lim_(x\to-2^-)√(-1-x)+2=√(-1+2)+2=√(1)+2=1+2=3`
`\lim_(x\to-2^+)f(x)=\lim_(x\to-2^+)2x+7=2(-2)+7=-4+7=3`
`\lim_(x\to-2)f(x)=\lim_(x\to-2)2=2`

Final answer:

Hence the final answer is

`\begin{gathered} 3 \\ \\ 3 \\ \\ 2 \end{gathered}`