Question

let the function $f$ be defined by:
f(x)=\begin{cases}x + 2&\text{if }x < - 2\\2&\text{if }x > - 2end{cases}
sketch the graph of this function and find the following limits, if they exist.
()

1. $lim_{x

ightarrow - 2^{-}}f(x)=$

1. $lim_{x

ightarrow - 2^{+}}f(x)=$

1. $lim_{x

ightarrow - 2}f(x)=$

Explanation:

Step1: Left - hand limit

For $x\to - 2^{-}$, use $f(x)=x + 2$. So $\lim_{x\to - 2^{-}}f(x)=\lim_{x\to - 2^{-}}(x + 2)=-2+2 = 0$.

Step2: Right - hand limit

For $x\to - 2^{+}$, use $f(x)=2$. So $\lim_{x\to - 2^{+}}f(x)=2$.

Step3: Overall limit

Since $\lim_{x\to - 2^{-}}f(x)
eq\lim_{x\to - 2^{+}}f(x)$, $\lim_{x\to - 2}f(x)$ does not exist.

Answer:

1. $0$
2. $2$
3. Does not exist