Question

Find the indicated limit, if it exists. 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 27 minus x when x is greater than or equal to 9
The limit does not exist.
18
0
9

Answer 1

Answer:

B. 18

Step-by-step explanation:

For the function

$f(x)=\left\{\begin{array}{l}x+9,\ \ x$

we can find the value of the function for all x that are very close to 9 but are less than 9 and for all values of x that are very close to 9 but are greater than 9.

1. For $x$

$\lim \limits_{x\rightarrow 9}f(x)=\lim \limits_{x\rightarrow 9}(x+9)=9+9=18$

2. For $x\ge 9:$

$\lim \limits_{x\rightarrow 9}f(x)=\lim \limits_{x\rightarrow 9}(27-x)=27-9=18$

So, limit exists and is equal to 18.