Answer:
Step-by-step explanation:
For the limit of a function to exist, then the right hand limit of the function must be equal to its left hand limit as shown;
If the function is f(x), for f(x) to exist then;
[tex]\lim_{n \to a^{+} } f(x) = \lim_{n \to a^{-} } f(x) = \lim_{n \to a } f(x)[/tex]
Given the function;
[tex]f(x) = \left \{ {{x+9\ x<9} \atop {9-x \ x \geq 9}} \right\\[/tex]
Lets check if the above statement is true.
The right hand limit of the function occurs at x> 9
f(x) = 9-x
[tex]\lim_{x \to 9+} (9-x)\\= 9-9\\= 0[/tex]
The left hand limit occurs at x<9
f(x) = x+9
[tex]\lim_{x \to 9^{-} } (x+9)\\= 9+9\\= 18[/tex]
From the above calculation, it can be seen that [tex]\lim_{x \to 9^{+} } f(x) \neq \lim_{x \to 9^{-} } f(x)[/tex], this shows that the function given does not exist at the given point.
