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.

The limit exists

Step-by-step explanation:

First note that for a function to exist, it must be continuous at the point given.

A function therefore said to be continuous if the right hand limit is equal to the left hand limit and equal to the limit of the function at the point x = x0 where x0 is the value of x which the limit is tending towards.

According to the question, the right hand limit function is the corresponding function at when x>-10. The corresponding function is f(x) = x+16

Substituting x = -10 into the function we have;

f(-10) = -10+16

f(-10) = 6

This shows that the right hand limit is 6.

The left hand limit function is the corresponding function at when x<-10. The function is f(x) = -4-x

Substituting x = -10 in the function, we will have;

f(-10) = -4-(-10)

f(-10) = -4+10

f(-10) = 6

This shows that the left hand limit is also 6.

As it can be seen that the corresponding value of the limit at x = -10 is also 6.

Based on the conclusion, since the right hand limit = left hand limit = limit of the function at the point, therefore, the limit of the function is continuous and since since all continuous functions exists, the function above exists

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,