## anonymous 5 years ago Use the graph to determine each limit.

1. anonymous

i) $\lim_{x \rightarrow 2^{-}} f(x)$ ii) $\lim_{x \rightarrow 2^{+}} f(x)$ iii) $\lim_{x \rightarrow 2} f(x)$ iv) $\lim_{x \rightarrow 2^{-}} f(x)$ v) $\lim_{x \rightarrow 0^{+}} f(x)$ vi) $\lim_{x \rightarrow 0} f(x)$

2. anonymous

ERRATA: iv) $\lim_{x \rightarrow 0^{-}} f(x)$

3. amistre64

lets call the left graph "f(x)" and the right graph "g(x)" that way we can tell what were talking about.... now are we supposed to take the specified limit as it pertains to both graphs individually?

4. anonymous

we must answer all for each graph.

5. amistre64

so the limits are 2 from the right, 2 from the left, 0 from the right, 0 from the left, and at 0 and at 2..if I read this correctly

6. anonymous

Yes, that's correct.

7. amistre64

a = f(x) lim{2+} = +infinity; lim{2-} = -infinity; lim{2} = not exist.

8. amistre64

a = f(x) lim{0+} = 0; lim{0+} is undefined, no graph there; lim{0} = 0 maybe...but hard to tell since the 0- is gone....

9. anonymous

you mean, lim{0-} is undefined, right?

10. amistre64

umm.... yeah, thats what I meant :)

11. anonymous

ohh! thanks! I do not know how to define it. let's b.

12. amistre64

b=g(x) lim{2+} = -1; lim{2+} =-1 ; lim{2} = -1 lim{0+}=1; lim{0-}=undefined; lim{0}=1 I would assume since it is a solid "dot"

13. amistre64

did it again didnt i....lim{2-} = -1

14. anonymous

haha. np. btw, thanks!

15. amistre64

youre welcome :)