Question

I need help with a limit question PRECALC! will give medal to person that helps and explains.
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 9 minus x when x is greater than or equal to 9

Answer 1

It's easiest if you can draw a graph of f(x).

Answer 2

it doesn't make sense though. does it not exist @ospreytriple

Answer 3

Your graph will tell you right away. You'll have one line (y=x+9) from (-infinity, 9) and another line (y=9-x) from [9, infinity). Now, imagine the limit as you approach x=9 from the left. That's the left hand limit. And imagine the limit as you approach x=9 from the right. That's the right hand limit. If the LH limit and the RH limit aren't the same, then the limit doesn't exist at x=9. Make sense?

Answer 4

In other words, When x=9, what is the value of y=x+9. That's the LH limit. What is the value of y=9-x when x=9. That's the RH limit. Are theyb the same?

Answer 5

is it 18?

Answer 6

Sorry, no. Were you able to draw a graph?

Answer 7

yeah but I got 18? what am I doing wrong?

Answer 8

@ospreytriple sorry im just soo confused

Answer 9

how did you get that?

Answer 10

I think this is a better picture

Answer 11

it has to be 18?

Answer 12

@gatorgirltj ?

Answer 13

9+9 =18<9.... wait no is it 0

Answer 14

it doesn't make sense my choices are (does not exist, 9, 18 , 0) I ruled out 9 and dne so its one of the others

Answer 15

Did you look at my graph?

Answer 16

that's the problem. and yes I did. that's why im lost

Answer 17

Your initial question says f(x) = 9-x for x>=9. Which is correct?

Answer 18

no its 9+x or rather X+9

Answer 19

I thought that was for x<9??

Answer 20

I messed up the second half im sorry my bad its 27-x x>9
im so sorry

Answer 21

OK. So it's f(x) = x+9 for x less than 9, and f(x) = 27-x for x greater than or equal to 9. Is that correct?

Answer 22

yes!

Answer 23

Terrific. I'm going to attach a new graph. Trace the red line from the left, and trace the blue line from the right. Do both lines approach the same value as they get to x=9?

Answer 24

18 right?

Answer 25

Yayyyyyyyy! Sorry for the mix-up but I was working with the wrong function initially. So, if the limits as you approach from the left side and as you approach from the right side are the same, the limit exists and it is that value. If the LH and RH side approach different values (my first graph), then the limit doesn't exist.

Answer 26

wait was I right or no? I already put DNE and it said wrong on my practice test and idk how to fix it to make it right I did the math by pluging it in and got 18,

Answer 27

You were correct.

Answer 28

The correct answer is 18.

Answer 29

SWEET!! okay help me with one more please @ospreytriple

Answer 30

Sure, go ahead