anonymous 3 years ago Use the information to evaluate the limits. I have a drawing attached.

1. anonymous

|dw:1342983331687:dw|

2. anonymous

@apoorvk Let me draw out the options from which I have to answer.

3. anonymous

|dw:1342983428659:dw|

4. anonymous

we can do one at a time .there are 4. but heres A^

5. anonymous

@apoorvk ?

6. anonymous

That's: lim [4 f(x)] ---> right? x ->c and [.] represents greatest integer function (GIF) - right?

7. anonymous

Yes, and I think?

8. anonymous

Ohkay... so.. that basically means I guess: |dw:1342983884987:dw| You have the value of that limit inside provided, you need to plug it in and proceed - understandable?

9. anonymous

yeah

10. anonymous

so would it be lim f(4)?

11. anonymous

umm no, actually, that's 4 times the limits - $[4 \times \lim \limits_{x\rightarrow c}^{}f(x) ]$

12. anonymous

Oh okay, how would I solve that?

13. anonymous

and $$\lim \limits_{x\rightarrow c}^{}f(x) = 3/2$$ is already given!

14. anonymous

Ok

15. anonymous

so what would we do divide 4?

16. anonymous

im confsued.. what do we do

17. anonymous

@apoorvk

18. anonymous

Cool down your nerves - nothing to get confused about! :) (ain;t no monster :P lol) I just brought the whole limit expression inside the GIF brackets - we can do that since it will not affect the limit value). Then, since $$\large \lim\limits_{x \rightarrow t}k.f(x) = k.\lim\limits_{x \rightarrow t}f(x)$$, for any function f(x) and constant k, I take the '4' out of the limit, and I end up with: $[ 4.\lim\limits_{x \rightarrow c}f(x)]$

19. anonymous

lol. Ok so for a, we still have [4 lim f(x)] as x approaches c.. ok

20. anonymous

Now it's given (in your first whiteboard drawing above) that $$\lim \limits_{x\rightarrow c}f(x) = 3/2$$, I substitute that value into $$[4\lim \limits_{x\rightarrow c}f(x)]$$, an hence now I get: $4 \times (3/2)$

21. anonymous

Yes, ok

22. anonymous

So then a is: 6?

23. anonymous

Can I write b now?

24. anonymous

yes! sure

25. anonymous

Kk im drawing now!

26. anonymous

|dw:1342985761573:dw|

27. anonymous

Is it just 2? I'm not sure

28. anonymous

hey I need to make one thing sure - is that [.] for a step-up function or just general brackets?

29. anonymous

if nothing's been stated, they're probably just general brackets~

30. anonymous

what do you mean, sorry

31. anonymous

Its lim [4f(x)] for a.

32. anonymous

has anything been stated for those square brackets? If not am guessing they are just normal parenthesis, and not for GIF - in that case the second one would be 2 alright!

33. anonymous

So a is still 6? and b is 2? lim [4f(x)] for a is exactly how it written

34. anonymous

because:|dw:1342986392700:dw|

35. anonymous

ok cool! so far i have a as 6, b as 2. Ill write c now

36. anonymous

|dw:1342986644322:dw|

37. anonymous

See, if [.] represents GIF, it should be mentioned, because in my education system, the rule is generally they would mention it if it is for a GIF - I am not sure about how's it stated in Us schools.

38. anonymous

ok I wrote c. it says; lim[f(x)g(x)] as x-->c

39. anonymous

Okay here you use the funda: |dw:1342986659285:dw|

40. anonymous

Ok so would c be 3/4?

41. anonymous

?

42. anonymous

yeah right!

43. anonymous

yay! ok heres d

44. anonymous

|dw:1342987062541:dw|

45. anonymous

lim f(x)/g(x) as x--> c = ??

46. anonymous

okay same way as the others - can you try this? You need to separate the two limits and then divide them.

47. anonymous

Ok would it be 3?

48. anonymous

|dw:1342987382978:dw|

49. anonymous

Yeah right! good work!

50. anonymous

thanks so much

51. anonymous

no worries :]