Consider the function give below
f(x)={ 0, x less then or equal to -2
{ sin 1/x+2 , x> -2
does the lim x->-2+ exist?

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

We have a function defined by pieces

f(x)=0 if

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

Now for the right-side limit

Since both limits are different, the required limit does not exist

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step-by-step explanation: