Question

Find the indicated limit, if it exists. limit of f of x as x approaches negative 10 where f of x equals negative 4 minus x when x is less than negative 10, 6 when x equals negative 10, and x plus 16 when x is greater than negative

10
6
0
16
The limit does not exist.

Answer 1

The answer is 6. Here's why:

This function is defined in pieces. To find the limit as x approaches -10 we need to evaluate the limit as x approaches -10 from the right and from the left. In order for the limit to exist at x=-10 the left-hand limit and right-hand limit must be equal. Furthermore, they should be equal to the value of the function at -10. Here f(-10)=6.

Let's find the limit as x approaches -10 from the left. Here the values of x would be less than -10. That is x<-10 so we use f(x)=-4-x making the limit -4--10=-4+10=6

Let's find the limit as x approaches -10 from the right. Here the values of x would be greater than -10. That is x>-10 so we use f(x)=x+16 making the limit -10+16=6

Since the lmit from the right and from the left are equal and they also equal the value of the function at x=-10, the limit is 6.
`lim`