Answer:
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
