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

No solution because it makes the most sense

Answer 2

The limit exists

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