## roselin 3 years ago 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

1. roselin

|dw:1351353752666:dw|

2. ilikephysics2

The second one

3. roselin

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

4. roselin

How do I solve it?

5. goformit100

yes the second one

6. roselin

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

7. roselin

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

8. henpen

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).

9. henpen

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

10. henpen

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

11. roselin

oh okay< and what about the 2nd one?

12. henpen

It's the opposite of (1)

13. roselin

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

14. henpen

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

15. roselin

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

16. henpen

Yes

17. roselin

okay, thank you so much.