## AmTran_Bus one year ago Limit question?

1. AmTran_Bus

|dw:1436286205012:dw|

2. AmTran_Bus

Um. Here are my choices but Im getting DNE

3. AmTran_Bus

4. AmTran_Bus

What in the world someone help! http://www.wolframalpha.com/input/?i=limit+as+x+approaches+0+%28e%5Ex-6%29%2Fsin+4x

5. AmTran_Bus

The problem does not say from the left or right!!!!!!!!! So my DNE is right but what do I do?

6. SolomonZelman

$$\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\frac{e^x-6}{\sin(4x)}}$$ ?

7. AmTran_Bus

Correct

8. welshfella

would l'hopitals rule be helpful here?

9. AmTran_Bus

Good thought. Let me try it

10. SolomonZelman

can't do it yet

11. SolomonZelman

it is not 0/0 when you plug in x=0

12. welshfella

right - only the denoiminator = 0 l'hopitals no help

13. AmTran_Bus

Oh yea, must be inf/inf or 0/0

14. welshfella

as x approaches 0 sin 4x approaches 0 and e^x - 6 approaches -5 so can we then say that the limit is - infinity?

15. welshfella

- approaching from above 0

16. SolomonZelman

you are right, the limit actually doesn't exst.

17. AmTran_Bus

Yea, thats what has thrown me off for a long time. But wolfram treats it as 0+ and 0- and and the answer choices have both neg inf and pos inf

18. SolomonZelman

even one sides limits diverge

19. SolomonZelman

when you get a limit that is equal to +∞ or -∞, that means the limit does NOT exist. (It is infinite - not limited)

20. AmTran_Bus

But it is an ans choice!

21. SolomonZelman

Well, for two sides limit, it DNE

22. AmTran_Bus

I agree

23. SolomonZelman

from the right side it is ∞, from the left side it is -∞

24. AmTran_Bus

dumb problem and ans choices

25. SolomonZelman

do you have an answer choice does not exist?

26. AmTran_Bus

27. welshfella

yes near the y axis the graph looks like |dw:1436287092439:dw|

28. AmTran_Bus

@SolomonZelman

29. AmTran_Bus

@welshfella so do you agree DNE?

30. welshfella

yes

31. AmTran_Bus

Well thanks for all your help! I may email prof

32. AmTran_Bus

Well, I asked on yahoo ans and they said -inf. I just dont see it but gotta mark something @hartnn @SolomonZelman @welshfella

33. hartnn

limit shouldn't exist sin 4x is negative when x<0 and it is positive when x>0 hence Left hand limit would not = right hand limit

34. AmTran_Bus

I agree hartnn. Just these ans choices giving fit.

35. SolomonZelman

ok, maybe the question is a little bit different?

36. AmTran_Bus

??

37. SolomonZelman

Are you sure it is exactly saying $$\Large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\frac{e^x-6}{\sin(4x)}}$$

38. SolomonZelman

well, then this limit doesn't exist.

39. SolomonZelman

I mean if limit=∞ or -∞ it doesn't exist (either way)

40. hartnn

people saying -infinity are assuming that sin4x = 0 e^x -6 will be negative

41. SolomonZelman

ohh...

42. SolomonZelman

yeah, should have noticed that:)

43. SolomonZelman

Bus?

44. AmTran_Bus

I'm here! So is it -inf after all?

45. SolomonZelman

yes

46. AmTran_Bus

Sin 4x=0?

47. SolomonZelman

yes

48. hartnn

no lol, the limit is still DNE. In yahoo answer, they might have said -inf as they might have assumed sin4x =0 ... that was my point, but sin 4x is not actually 0

49. SolomonZelman

well, if you take the limit of sin(4x) as x→0 alone, then it is 0

50. AmTran_Bus

Story of my life...

51. hartnn

why would you do that lol...

52. SolomonZelman

1 D, XD = (1+x)D

53. SolomonZelman

jk

54. SolomonZelman

idk, hartnn

55. AmTran_Bus

Gonna email prof

56. SolomonZelman

the limit is indeterminate, beause you are trying to divide by zero

57. SolomonZelman

technically u r...

58. SolomonZelman

when you divide by a number that approaches 0 from the right, you get ∞, and when you divide by a number that approaches 0 from the left, you get -∞. if the divident is positive. In this case divident is negative, so it is the other way around. when you divide by a number that approaches 0 from the right, you get -∞, and when you divide by a number that approaches 0 from the left, you get ∞. And if you take a 2-sides limit (as in your case), you shouldn't get just ∞ or -∞.....