## anonymous one year ago Use the given graph to determine the limit, if it exists. -2; 6 1; 1 Does not exist; does not exist 6; -2

1. anonymous

2. anonymous

find

3. freckles

Do you know how to evaluate f(2.1)?

4. freckles

from looking at the graph

5. anonymous

nope @freckles

6. ganeshie8

|dw:1438030387764:dw|

7. anonymous

@ganeshie8 help

8. ganeshie8

Imagine you're walking on the graph, towards x=2, from the right side : |dw:1438030518779:dw|

9. anonymous

ok so what do i do next? @ganeshie8

10. ganeshie8

what value does the graph takes as you approach x=2 ?

11. anonymous

idk 2? @ganeshie8

12. ganeshie8

careful, values down that horizontal axis are negative so i think you mean -2 ?

13. anonymous

yes. so is that the final answer? -2? @

14. ganeshie8

|dw:1438030838624:dw|

15. ganeshie8

Yes, so we say the limit from right hand side of x=2 is $$-2$$ and we write it mathematically as : $\Large \lim\limits_{x\to2^{+}}~~f(x)~~~=-2$

16. ganeshie8

see if you can guess the limit from left hand side : $\Large \lim\limits_{x\to2^{\color{red}{-}}}~~f(x)~~~= ?$

17. anonymous

would it be 6? @ganeshie8

18. ganeshie8

Perfect! You do knw these things!

19. anonymous

so the answer is -2;6 @ganeshie8

20. freckles

And if you notice f is approaching -2 if you plug in values to the right of x=2 like f(2.5)=-2 f(2.3)=-2 f(2.1)=-2 These numbers don't all usually appear the same but these numbers are approaching -2 as x approaches x=2 you can do the same thing for the left... also I know f(2.1)=-2 from just looking at: |dw:1438031090291:dw|

21. freckles

and also I probably could have drawn 2.1 closer to 2 but it is kind of hard to draw it closer to 2.1 without making it ugly and not readable