Which of the following statements about the function y=f(x) graphed here are true, and which is false?
lim f(x) does not exist
x goes to 2
2) lim f(x) =2
x goes to 2
3) lim f(x) does not exist
x goes to 1
4) lim f(x) exists at every point Xo in (-1,1)
X goes to Xo
5) lim f(x) at every point Xo in (1,3)
X goes to Xo

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- anonymous

- katieb

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- anonymous

|dw:1351353752666:dw|

- anonymous

The second one

- anonymous

that's the figure
I posted the questions before posting the figure

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- anonymous

How do I solve it?

- goformit100

yes the second one

- anonymous

what do you mean by second one? i am sorry, I did not get it

- anonymous

I am not getting why u guys are saying, "thesecond one"

- anonymous

The places where the function does crazy things like not having a value (indicated by an empty circle), or suddenly jumps from one y-value to another are called discontinuities (because of them you can't draw the function in a nice line without pen leaving paper).
Because they are slightly awry, these places don't have limits, as when x approaches them the function doe *not* settle down to a nice value (which is what the limit is, it asks: 'as x gets close to a, does y get closer to ONE value in particular?'- the limit's value is actually this settling down value, call it b).

- anonymous

(1) is incorrect, as the function is nice at x=2
(3) is correct, same reason
4 and 5 are obviously incorrect

- anonymous

Although I say that, I'm not sure about 3 as it may not have a limit approaching it from both sides, so 3 is probably incorrect

- anonymous

oh okay< and what about the 2nd one?

- anonymous

It's the opposite of (1)

- anonymous

it means when x goes to 2 , y =s 2?

- anonymous

Yes. I'm not sure whether it matters that there is no line right of that.

- anonymous

okay, just for clarification. f(x) means y right?

- anonymous

Yes

- anonymous

okay, thank you so much.

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