Christos Group Title Can you help me find this limit: http://screencast.com/t/6CD9ErAG3N9m All I need is the first step, I am gonna climb from there easily. Sorry if it's a little unclear picture, it's from an old book one year ago one year ago

1. Christos Group Title

@ganeshie8 @Mertsj

2. robz8 Group Title

for reference, the answer is $-\sqrt3/2$ i do not remember the steps though, sorry

3. Christos Group Title

I know the answer too my friend, but I dont know how to find it, thanks though

4. robz8 Group Title

sorry i could not help :/

5. Stewie_Griffin_ Group Title

CANT EVEN SEE THE QUESTION

6. Christos Group Title

How Come?? The guy above you saw it , I posted a picture

7. Jhannybean Group Title

I can't see it either. what is the limit going to? Can't make it out after the arrow

8. Christos Group Title

infinity+ ....

9. Christos Group Title

+ infinity ***** I am sorry

10. robz8 Group Title

lim of x going to positive infinity of sin((pi*x)/(2-3x))

11. Jhannybean Group Title

$\lim_{x \rightarrow +\infty}\sin (\frac{ \pi x }{ 2-3x })$

12. Stewie_Griffin_ Group Title

can you actually take the pic clearly?

13. rajee_sam Group Title

$\lim_{x \rightarrow +\infty} Sin (\frac{ \pi x }{ 2-3x })$

14. Christos Group Title

Yes

15. Jhannybean Group Title

Now Stewie can stop trolling, lol. xD

16. Stewie_Griffin_ Group Title

VICTORY?

17. rajee_sam Group Title

I want to learn this too

18. Jhannybean Group Title

Same here.

19. Stewie_Griffin_ Group Title

yes or no?

20. rajee_sam Group Title

who is teaching??

21. Jhannybean Group Title

You can divide by the highest power in the denominator which is x

22. Christos Group Title

But how does that lead you to the solution which is -sqrt(3)/2

23. Jhannybean Group Title

Can't you? $\large \lim_{x \rightarrow +\infty}\sin(\frac{ \pi x/x }{ \frac{ 2 }{ x }-\frac{ 3x }{ x } })$

24. Christos Group Title

yes and then?

25. Jhannybean Group Title

So what is $\sin(-\frac{ \pi }{ 3 })$? Whcih quadrant is sine negative ?

26. rajee_sam Group Title

$\lim_{x \rightarrow +\infty} \sin \frac{ x }{ x }(\frac{ \pi }{ \frac{ 2 }{ x } - 3 })$

27. Christos Group Title

@myko @timo86m @jim_thompson5910 @jhonyy9 @Hero @Euler271

28. Christos Group Title

The result is most likely engative yea

29. rajee_sam Group Title

Sin (- pi / 3)

30. Christos Group Title

negative*

31. Christos Group Title

yes but HOW @rajee_sam

32. Jhannybean Group Title

Sine is negative in quadrant 3 and 4, so if $\sin \frac{ \pi }{ 3 } = \frac{ \sqrt{3} }{ 2 }$ then $\sin -\frac{ \pi }{ 3 }= -\frac{ \sqrt{3} }{ 2 }$

33. Christos Group Title

Am I eligible to differantiate this thing ? because if we differantiate we get sin(pi/-3)

34. Christos Group Title

instantly

35. rajee_sam Group Title

|dw:1369516434913:dw|

36. Jhannybean Group Title

You just need to find the positive radian measure, which is $\frac{ \pi }{ }$ and then translate it accordingly to find which negative value is correlated with the positive radian measure

37. rajee_sam Group Title

$\sin ( -\theta ) = - \sin (\theta)$

38. Jhannybean Group Title

sorry,i meant pi/3 *

39. Christos Group Title

how did you get the x out @rajee_sam

40. rajee_sam Group Title

I am taking a GCF for both numerator and denominator so that I can cancel them out and do not have any x multiplied with anything

41. Christos Group Title

GCF ?

42. rajee_sam Group Title

Common Factor

43. phi Group Title

$\lim_{x \rightarrow +\infty}\sin \left(\frac{ \pi x }{ 2-3x }\right) = \sin\left( \lim_{x \rightarrow +\infty} \frac{ \pi x }{ 2-3x }\right)$ as noted above you can rewrite $\frac{ \pi x }{ 2-3x } = \frac{ \pi }{\frac{2}{x} -3}$

44. Christos Group Title

Alright! Alright! I solved it this way! By during the time I was trying to solve this I figured out a second way! Tell me if this is correct: Just taking the derivative of both denominator and numerator and then we are done. Can I apply this to ANY limit? Because here it works!

45. Jhannybean Group Title

that's what i did pi.... :(

46. Christos Group Title

@phi

47. Jhannybean Group Title

if you're taking the derivative you'll have to use chain rule on the whole thing, sin (whatever's inside) and then * whatever is inside.

48. phi Group Title

yes, you can use L'Hopital's rule http://en.wikipedia.org/wiki/L'Hôpital's_rule if you get 0/0 or inf/inf

49. Christos Group Title

and no chain rule??

50. Christos Group Title

51. phi Group Title

no, use chain rule. use $\lim_{x \rightarrow +\infty}\sin \left(\frac{ \pi x }{ 2-3x }\right) = \sin\left( \lim_{x \rightarrow +\infty} \frac{ \pi x }{ 2-3x }\right)$

52. phi Group Title

*do not use chain rule

53. Christos Group Title

but even if I dont use the chain rule we end up to the same result

54. Christos Group Title

Ohh so this formula you showed to me just now is only when we have 0/0 or infinite/infinite ?

55. Jhannybean Group Title

Oh I see, and you'd use LH rule to simplify it further and end up with the same result.

56. phi Group Title

using L'Hopital's rule needs 0/0 or inf/inf use it on $\lim_{x \rightarrow +\infty} \frac{ \pi x }{ 2-3x }$

57. Christos Group Title

ok and I get this http://screencast.com/t/jPlMQFrZ What now?

58. phi Group Title

you can use L'Hopital d top/ d bottom = pi/-3 or you can use algebra

59. Christos Group Title

and the lim(x-->+infinity) goes away?

60. Christos Group Title

oh I get you now

61. Christos Group Title

but still I am stuck on the lim thingy

62. phi Group Title

then sin (-pi/3) = -sqrt{3}/2 *** and the lim(x-->+infinity) goes away? if you use L'Hopital $\lim_{x \rightarrow +\infty} \frac{ \pi x }{ 2-3x } = \lim_{x \rightarrow +\infty} \frac{\pi}{-3}= -\frac{\pi}{3}$

63. Christos Group Title

I see, thank you all