## anonymous 4 years ago whats the lim x goes to infinity of 2/square root of x

1. anonymous

0

2. anonymous

yes

3. zepdrix

Rose if you're not convinced, just plug a large number into your calculator to check! :) if you plug one bajillion in for x, what value do you get for the limit? $\frac{ 2 }{ \sqrt{bajillion} }\approx \frac{ 2 }{ 999999999 } \approx 0$

4. anonymous

yeah, but do what zepdrix said only for check, because if you do this in a test for example, it will be wrong because infinity is NOT a number...

5. anonymous

okay

6. anonymous

it is always 0 ?

7. anonymous

no! it will depends on what you are taking the limit, always try to simplify the limit, try to do not have a denominator, in this case we can not simplify so we do this

8. anonymous

i am trying to solve this problem where x goes to infinity 2+square root of x/ 2- square root of x

9. anonymous

i am getting the answer as 1, is it right?

10. anonymous

$\lim_{x \rightarrow \infty}\frac{2+\sqrt{x}}{2-\sqrt{x}}$

11. anonymous

this one?

12. anonymous

yes,

13. anonymous

the limit is equal to -1

14. anonymous

have you already study L'hospital rule ?

15. anonymous

can you please explain how you got -1?

16. anonymous

No,

17. anonymous

ok let me explain

18. anonymous

|dw:1350703643878:dw|

19. anonymous

got it?

20. anonymous

what did you do with the whole numerator thing? u ended up with X

21. anonymous

when x goes to infinity, the other terms with lower power we take them off, and stay only with the higher terms them simply if possible and aply the limit

22. anonymous

i will post how i got the numerator

23. anonymous

ohh , u mean the limit of 4 and 4 sqrt x = 0?

24. anonymous

|dw:1350704041192:dw|

25. anonymous

no this i simply take them out because comparing with infinity they make no difference

26. anonymous

oh okay,

27. anonymous

when you deal with limits on the infinity you can make this assumptions

28. anonymous

but take care...

29. anonymous

when you see L'hostpital's Rule this limits will became very easy to solve.... you will see

30. anonymous

we have not gotten to that yet.

31. anonymous

yeah

32. anonymous

if you do not mind then, I have one more problem. would you explain that one?

33. anonymous

sure

34. anonymous

thank you

35. anonymous

lim sec x x goes to( -pi/2)^+

36. anonymous

let me solve here one moment

37. anonymous

okay

38. anonymous

it is equal to infinity, i will draw here

39. anonymous

okay

40. anonymous

|dw:1350704691784:dw|

41. anonymous

is it clear?

42. anonymous

yes,viewing it.

43. anonymous

see, when we have something divide by a number really really really small them it becomes a really really really large number so the limit tends to the infinity

44. anonymous

okay, but how did you get that 10?

45. anonymous

it is just a notation for this: 0.00000000000000000000000...00000000000001, then we represent this really small or large number with 10 power

46. anonymous

oh ,okay. got it.

47. anonymous

wait,wait

48. anonymous

that (-pi/2)^+ is the same as (-pi/2)?

49. anonymous

ALMOST the same, when we have this + is a little more than pi/2

50. anonymous

-pi/2, sorry

51. anonymous

so, the asnwer will be the same one right?

52. anonymous

53. anonymous

no, because if we take 1/0 it is not allowed. But 1/0.00000000001 is allowed

54. anonymous

we can not divide by 0, NEVER

55. anonymous

yes,that is true.

56. anonymous

so you got it?

57. anonymous

yeah.

58. anonymous

Thank you soooo much.

59. anonymous

yw :)

60. anonymous

good night, byee

61. anonymous

good, bye

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