## Dido525 Group Title Find the values of a and b so that the following is true. one year ago one year ago

1. Dido525 Group Title

I am thinking about L'Hospital's rule but I am not sure how I would apply it...

2. Rezz5 Group Title

well, you can separate them, then solve them

3. Dido525 Group Title

Yeah.... But I have two variables then.

4. Rezz5 Group Title

are you sure it tends to infinity?

5. Dido525 Group Title

Yep.

6. Dido525 Group Title

0.

7. Dido525 Group Title

oops.

8. Rezz5 Group Title

why two variables?

9. Rezz5 Group Title

if you differentiate the variable you get nothing from a, but b will still be present, you can get b right?

10. Dido525 Group Title

$\lim_{x \rightarrow 0} (\frac{ \sin(2x) }{ x^3 }+a+\frac{ b }{ x^2 })=0$

11. Dido525 Group Title

Yeah. I think you are right.

12. Rezz5 Group Title

ahhh, so it tends to zero?

13. Dido525 Group Title

Yep :P . I typed wrong.

14. Rezz5 Group Title

no problem, you can separate them then do the limits, you can spot it by inspection, very easily

15. Dido525 Group Title

Hmm Let me try...

16. Rezz5 Group Title

have you done it?

17. Dido525 Group Title

I can't solve the limit of: $\lim_{x \rightarrow 0}\frac{ \sin(2x) }{ x^3 }$

18. Rezz5 Group Title

you can!! differentiate 3 times until the denominator is 1,

19. Rezz5 Group Title

not 1, differentiate until the denominator is a constant

20. Rezz5 Group Title

sin(2)=2sin(x)cos(x)

21. Dido525 Group Title

I got -4/3 .

22. Rezz5 Group Title

for?

23. Dido525 Group Title

The limit.

24. Rezz5 Group Title

sin(2x)/x^3 as x tends to infinity?

25. Rezz5 Group Title

how ?

26. Dido525 Group Title

To 0 :P .

27. Rezz5 Group Title

lol!!! im losing it today...

28. Rezz5 Group Title

but still, i would have thought it was zero

29. Dido525 Group Title

Waitt.

30. Dido525 Group Title

The Limit is infinity..... :( .

31. Rezz5 Group Title

yep,

32. Dido525 Group Title

We can't solve anything then.

33. Rezz5 Group Title

we could, i mean if one of the variables was infinity

34. Dido525 Group Title

But We can't do anything with infinity.... It's not a number.

35. Rezz5 Group Title

wait are you sure it should tend to 0?

36. Dido525 Group Title

Well I would assume it should tend to a finite value.

37. Rezz5 Group Title

i suspect the limit should tend to infinity then for it so satisfy the limit

38. Rezz5 Group Title

not necessarily, it can be infinity, let assume it was infinity, then we can do the question with ease. have you done analysis by any chance?

39. Dido525 Group Title

No.....

40. Dido525 Group Title

Here is the question.

41. Rezz5 Group Title

okay, no problem, assume it is infinity because i think you were right the first time round, if it was infinity just plug in infinity to the differential you had computed

42. Dido525 Group Title

If we did that then a would be infinity and b would not exist.

43. Rezz5 Group Title

b would, it would be x^2,

44. Rezz5 Group Title

one moment,

45. Dido525 Group Title

but since b^2 tends to infinity the whole thing would be 0.

46. Dido525 Group Title

x^2 sorry not b^2.

47. Rezz5 Group Title

which would be 0, at when b/x^2 as x ->0

48. Dido525 Group Title

Exactly. We can't work with that.

49. Rezz5 Group Title

we could, if b = 0,

50. Rezz5 Group Title

0/anynumber = 0

51. Dido525 Group Title

But it's not. B/x^2 is zero, not b.

52. Dido525 Group Title

We don't know what b is.

53. Rezz5 Group Title

a could be -infinity, then this would satisfy the limit

54. Dido525 Group Title

But infinity- infinity is not 0.

55. Rezz5 Group Title

yes it is

56. Dido525 Group Title

No it's not. Infinity is not a number. It's a concept.

57. Rezz5 Group Title

that is true, i moment, i am trying to multi task, i jst remembered the proof that it isnt,

58. Dido525 Group Title
59. Rezz5 Group Title

okay, you need to apply l'hpitals rule over and over again, i would recon, but first you need to put all the equation under one common factor so $=\frac{\sin(2x) + ax^{3} + bx}{x^{3}}$

60. Rezz5 Group Title

http://answers.yahoo.com/question/index?qid=20110406112720AARpKn1 here is a better and easier way of doing it the sint is taylor expansion i think, the rest is pretty self explanatory

61. Dido525 Group Title

Lol. THanks :P .