## sam0004 Group Title Lim as x approaches pi/6 of (sin(x)-sin(pi/6))/x-pi/6 2 months ago 2 months ago

1. myininaya Group Title

compare to definition of derivative

2. myininaya Group Title

$\lim_{x \rightarrow a}\frac{f(x)-f(a)}{x-a}=f'(a)$

3. sam0004 Group Title

So the limit would = 1?

4. myininaya Group Title

no

5. myininaya Group Title

what is f?

6. sam0004 Group Title

...?

7. myininaya Group Title

what is f(x) and what is a?

8. sam0004 Group Title

F(x)=sin(x), f(a)=sin(pi/6)

9. myininaya Group Title

so what is f'?

10. sam0004 Group Title

Cos(x)-cos(pi/6)?

11. myininaya Group Title

:( if f=sin(x), then f'=?

12. sam0004 Group Title

Cos(x)

13. myininaya Group Title

14. sam0004 Group Title

A=sin(pi/6)?

15. myininaya Group Title

$\lim_{x \rightarrow a}\frac{f(x)-f(a)}{x-a}=f'(a) \text{ or we could say it equals } =(f(x))'|_{x=a}$

16. myininaya Group Title

$\lim_{x \rightarrow \frac{\pi}{6}}\frac{\sin(x)-\sin(\frac{\pi}{6})}{x-\frac{\pi}{6}}=(\sin(x))'|_{x=\frac{\pi}{6}}$

17. myininaya Group Title

do you see all i'm trying to get you to do is use the definition of derivative

18. myininaya Group Title

you are suppose to determine f and a then find f' then plug a into f' to get the result you are searching for

19. sam0004 Group Title

Sqrt(3)/2?

20. myininaya Group Title

yep

21. sam0004 Group Title

Thank you

22. sam0004 Group Title

Any chance you can help with critical numbers?

23. myininaya Group Title

sure

24. sam0004 Group Title

F(x)=4x/x^2+1

25. sam0004 Group Title

I know i need the derivative

26. myininaya Group Title

do you mean 4x/(x^2+1)? Also what did you get for the derivative?

27. sam0004 Group Title

Yes. F'(x)=(-4x^2+4)/(x^2+1)^2

28. myininaya Group Title

thats great now find when F'=0 Also we don't have to worry when F' DNE because x^2+1 is always positive. so F'=0 when top=0 so when -4x^2+4=0 solve for x now

29. sam0004 Group Title

Sqrt(-1)

30. myininaya Group Title

I think you should retry solving -4x^2+4=0 I will give you a (you will get two real solutions)

31. sam0004 Group Title

...+or-sqrt(-1)

32. sam0004 Group Title

+or-sqrt(1)

33. myininaya Group Title

right sqrt(1)=1 so x=1 or x=-1

34. myininaya Group Title

those are the critical numbers for F.

35. sam0004 Group Title

Wow...

36. sam0004 Group Title

Find the intervals where f(x)=4/(x^+1) is increasing or decreasing.

37. myininaya Group Title

is that f(x)=4/(x+1)? like you weren't trying to write an exponent right?

38. sam0004 Group Title

I Find the derivative...then set the denominator equal to zero...put those numbers on a number line and plug in numbers to find the intervals?

39. sam0004 Group Title

I was writing an exponent

40. sam0004 Group Title

I apologize for missing the exponent

41. sam0004 Group Title

It should have said 4/(x^2+1)

42. myininaya Group Title

well I don't know what f you are looking at exactly. but yeah you definitely need to find f' because f' tells you if f is decreasing or increasing or neither f'=0 means the function is resting f'>0 means f is increasing f'<0 means f is decreasing I first find when f' =0 and when f' does not exist and then test each interval around those numbers to see if the function is increasing there or decreasing there

43. myininaya Group Title

so what is f' first?

44. sam0004 Group Title

-8x/(x^4+1)

45. sam0004 Group Title

X=-1 and x=1

46. myininaya Group Title

(x^2+1)^2 does not equal x^4+1

47. myininaya Group Title

just leave is at (x^2+1)^2

48. sam0004 Group Title

Increasing from negative infinity to 0 and decreasing from 0 to positive infinity

49. myininaya Group Title

also x^2+1 is always positive so f' and f exist everywhere so you just need to find when f'=0 which is when -8x=0 which is when x=?

50. myininaya Group Title

ok yep

51. sam0004 Group Title

F(x)=3x^2-12x=5 over the closed interval 0,3. Find absolute extrema.

52. sam0004 Group Title

Do i again begin with taking the derivative?

53. myininaya Group Title

see if there any critical numbers between 0 and 3 first

54. myininaya Group Title

which means you need to find f' which all means you need find when f'=0 this looks like you meant to write a polynomial so we don't need to worry when f' dne

55. sam0004 Group Title

X=2

56. myininaya Group Title

ok do F(0) and F(2) and F(3) which ever one of these are the lowest value is the absolute min value which ever one of these are the highest value is the absolute max value

57. sam0004 Group Title

Ok so you use the tow numbers in the interval and the critical number?

58. myininaya Group Title

also I don't know what your function is exactly critical numbers in between the critical numbers and any included endpoints just plug them back into the original function

59. myininaya Group Title

you have two equal signs

60. myininaya Group Title

i'm guessing that second equal sign is a + or a -

61. myininaya Group Title

can't decide which one

62. sam0004 Group Title

Should be +5

63. myininaya Group Title

ok do you want me to check your answers for this one or are you just going through problems and getting ideas on how to do them so you can pass your final

64. myininaya Group Title

like it seems like you are studying

65. sam0004 Group Title

I just need ideas on how to pass my final...i struggle with a few areas.

66. myininaya Group Title

67. myininaya Group Title

I have to go do some house stuff good luck on your final

68. myininaya Group Title