Answer:
The Limit doesn't exist
Step-by-step explanation:
One-Sided Limit
It's the term that describes when the limit of a function is computed as the variable approaches to a value from the right or from the left side.
They are expressed respectively as
[tex]\lim\limits_{x \rightarrow a^{+}}f(x)[/tex]
[tex]\lim\limits_{x \rightarrow a^{-}}f(x)[/tex]
We have a function defined by pieces
f(x)=0 if [tex]x\leq -2[/tex]
f(x)=sin(1/x)+2 if x > -2
For the limit when x approaches to -2 to exist, both one-sided limits must exist and be equal. Let's test the left-side limit
[tex]\lim\limits_{x \rightarrow -2^{-}}f(x)=0[/tex]
Now for the right-side limit
[tex]\lim\limits_{x \rightarrow -2^{+}}sin(1/x)+2=-sin(1/2)+2[/tex]
Since both limits are different, the required limit does not exist
