Question

Find the indicated limit, if it exists. (1 point) limit of f of x as x approaches 9 where f of x equals x plus 9 when x is less than 9 and f of x equals 9 minus x when x is greater than or equal to 9

Answer 1

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;

$\lim_{n \to a^{+} } f(x) = \lim_{n \to a^{-} } f(x) = \lim_{n \to a } f(x)$

Given the function;

$f(x) = \left \{ {{x+9\ x$

Lets check if the above statement is true.

The right hand limit of the function occurs at x> 9

f(x) = 9-x

$\lim_{x \to 9+} (9-x)\\= 9-9\\= 0$

The left hand limit occurs at x<9

f(x) = x+9

$\lim_{x \to 9^{-} } (x+9)\\= 9+9\\= 18$

From the above calculation, it can be seen that $\lim_{x \to 9^{+} } f(x) \neq \lim_{x \to 9^{-} } f(x)$, this shows that the function given does not exist at the given point.