## Christos 2 years ago 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

1. Christos

@ganeshie8 @Mertsj

2. robz8

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

3. Christos

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

4. robz8

sorry i could not help :/

5. Stewie_Griffin_

CANT EVEN SEE THE QUESTION

6. Christos

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

7. Jhannybean

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

8. Christos

infinity+ ....

9. Christos

+ infinity ***** I am sorry

10. robz8

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

11. Jhannybean

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

12. Stewie_Griffin_

can you actually take the pic clearly?

13. rajee_sam

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

14. Christos

Yes

15. Jhannybean

Now Stewie can stop trolling, lol. xD

16. Stewie_Griffin_

VICTORY?

17. rajee_sam

I want to learn this too

18. Jhannybean

Same here.

19. Stewie_Griffin_

yes or no?

20. rajee_sam

who is teaching??

21. Jhannybean

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

22. Christos

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

23. Jhannybean

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

24. Christos

yes and then?

25. Jhannybean

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

26. rajee_sam

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

27. Christos

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

28. Christos

The result is most likely engative yea

29. rajee_sam

Sin (- pi / 3)

30. Christos

negative*

31. Christos

yes but HOW @rajee_sam

32. Jhannybean

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

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

34. Christos

instantly

35. rajee_sam

|dw:1369516434913:dw|

36. Jhannybean

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

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

38. Jhannybean

sorry,i meant pi/3 *

39. Christos

how did you get the x out @rajee_sam

40. rajee_sam

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

GCF ?

42. rajee_sam

Common Factor

43. phi

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

44. Christos

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

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

46. Christos

@phi

47. Jhannybean

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

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

and no chain rule??

50. Christos

51. phi

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

*do not use chain rule

53. Christos

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

54. Christos

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

55. Jhannybean

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

56. phi

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

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

58. phi

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

59. Christos

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

60. Christos

oh I get you now

61. Christos

but still I am stuck on the lim thingy

62. phi

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

I see, thank you all