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Brrunno [24]
3 years ago
8

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
Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
6 0

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.

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