Given:
[tex]f(x)=\begin{cases}{\sqrt{-1-x}}+2\text{ }if\text{ }x<-2 \\ {2\text{ }} \\ {2x+7}\text{ }if\text{ }x>-2\end{cases}if\text{ }x=-2[/tex]
Required:
We have to find
[tex]\lim_{x\to-2^-}f(x),\text{ }\lim_{x\to-2^+}f(x),\text{ and }\lim_{x\to-2}[/tex]
Explanation:
[tex]\lim_{x\to-2^-}f(x)=\lim_{x\to-2^-}\sqrt{-1-x}+2=\sqrt{-1+2}+2=\sqrt{1}+2=1+2=3[/tex][tex]\lim_{x\to-2^+}f(x)=\lim_{x\to-2^+}2x+7=2(-2)+7=-4+7=3[/tex][tex]\lim_{x\to-2}f(x)=\lim_{x\to-2}2=2[/tex]
Final answer:
Hence the final answer is
[tex]\begin{gathered} 3 \\ \\ 3 \\ \\ 2 \end{gathered}[/tex]
