Find the indicated limit, if it exists. limit of f of x as x approaches 0 where f of x equals 5x minus 8 when x is less than 0 and f of x equals absolute value -4 minus x when x is greater than or equal to 0

The limit does not exist. Why? Because the left hand limit DOES NOT equal the right hand limit. Let’s double check:

We could use -0.000001 to represent the left hand limit. This is less than 0. We plug in 5x - 8

5(-0.000001) - 8
-0.000005 - 8
-8.000005
If we would continue the limit (extend the zeros to infinity), we would get exactly
-8
That is our left hand limit.

Our right hand limit will be represented by 0.000001. This is greater than 0. We plug in abs(-4 - x)

abs(-4 - (0.000001))
abs(-4.000001)
4.000001
If we would continue the limit (extend the zeros to infinity), we would get exactly
4

4 does not equal -8, therefore

The limit does not exist