Question

Can someone please help me don't remember how to do these problems

Answer 1

For f(x)= -x+3 x<2
3 for x=2
-x^2+6x-3 if x>2
Find lim f(x) as x approaches 2

Answer 2

Don't you have to check if it's defined first?

Answer 3

Defined? No.
You're supposed to use limits to figure this out,
but it really just boils down to plugging x=2 into the `left piece`,
and plugging x=2 into the `right piece`,
and seeing if they agree or not.

Answer 4

\[\Large\rm \lim_{x\to2^-}f(x)=\lim_{x\to2^-}-x+3\]

\[\Large\rm \lim_{x\to2^+}f(x)=\lim_{x\to2^+}-x^2+6x-3\]

Answer 5

I thought you needed to make sure f(a) was defined or whatever than check to make sure they agree on both sides, than f(a)=limit of f(a) or whatever?

Answer 6

f(a) must be defined,
and match both limits,
to `give us continuity`.

That isn't required for limit existing though.

Answer 7

Ohhhh yeah

Answer 8

I'm going a step ahead :P

Answer 9

But wait?

Answer 10

If it's says limit g(x) as x aprroaches 5 and the intervals for g(x) is x<-5 -5<x<5 and x>5 which one would I use

Answer 11

You would use both pieces surrounding x=5, ya?

Answer 12

So I guess middle and last pieces for that one.

Answer 13

Oh ok

Answer 14

And?

Answer 15

It would be two split answers? Or do we add them?

Answer 16

The left piece will give you a y-value,
the right piece will give you a y-value.

If they give you the same y-value, then that's your limit value.
If they don't give you the same y-value, then the limit does not exist.

Answer 17

Duhhhhhh omg!!!

Answer 18

Ok, I just needed to little refresher but I'm good now thank you Zepdrix :)

Answer 19

cool

Answer 20

Wait zep, g(5) and the limit of g(x) as x approaches 5 are the same right?!? I feel like they are trying to fool be and its making me second guess lol

Answer 21

:O

Answer 22

o_O

Answer 23

No. g(5) refers to the `dot at x=5`.
The limit of g(x) as x approaches 5 is the `line leading up to the dot`.

That's how I like to remember it at least.
The function value is the dot,
the limit is the line.

Answer 24

They aren't necessarily going to be the same.
That might end up being so though

Answer 25

So wait how would I figure it out than?

Answer 26

Like how could it be different

Answer 27

Like f(5) vs limit f(x) as x approaches 5

Answer 28

We finished this problem in Twiddla,
I didn't just leave her hanging as it appears.

In case anyone was wondering :D lol