Question

Find the indicated limit, if it exists.

Answer 1

In order for limit to exists at certain point, it must be continuous at that point.

Do you think function is continuous at x = 5?

Answer 2

How do I know if it is or not?

Answer 3

when you plug in the limit in the given function, the f(x) should be equal to 5, if f(x) not equal to 5 then it will not be continuous, that is what x=5 means
i hope this makes sense

Answer 4

But I don't know the limit

Answer 5

What? No. One way to determine if function is continuous at certain point. Let say x=a:
1. f(a) must exists.
2. \(\lim_{x\rightarrow a}f(x)\) must exists (remember to check both side)
3. \(f(a) = \lim_{x\rightarrow a} f(x)\)

Does that make sense? Try do number 2.

Answer 6

I don't really know how to do it still..

Answer 7

Ok, can you find \(\lim_{x\rightarrow5^{-}}f(x)\)? do you know how to do that? No?

Answer 8

No :( I'm sorry

Answer 9

it mean you just find limit from left side.

If it is possible, all you have to do is plug in whether it approach to (5)

function at x<5 is 5-x, right? just plug in 5 to that function.

Answer 10

does that make sense?

Answer 11

Oh okay so it's 0

Answer 12

yeah, so we know that: \[\lim_{x \rightarrow 5^{-}}f(x) = 0\]

Now find limit from right side. Do you know what it is?

Answer 13

would that be the one that says x+3?

Answer 14

right!

Answer 15

Should I plug 5 into it?

Answer 16

yeah

Answer 17

Okay so it's 8

Answer 18

right. now, in order for limit to exists, Limits from both sides must be same.

We now know that limits from left side is 0
and right side is 8.

Do you think limit exists?

Answer 19

No because they aren't the same

Answer 20

hooray

Answer 21

Right! So limit does not exist.

Answer 22

you are welcome :)

Answer 23

Thank you!!