## IsTim Group Title Find the equation of the tangent to the curve at the given x value. 2 years ago 2 years ago

1. IsTim Group Title

|dw:1335261368315:dw|

2. IsTim Group Title

I got up to this:|dw:1335261401688:dw|

3. IsTim Group Title

|dw:1335261446849:dw|

4. chaise Group Title

Calculate the derivative of the equation, make the equation to equal, solve it and plug in your x value. Are you familiar with the quotient rule in derivatives?

5. IsTim Group Title

Deriatives is f'(x) right? we're not doing that yet.

6. IsTim Group Title

Methods we're using is substitution, factoring and the conjugate method.

7. IsTim Group Title

I'm using the Calculus Phobe videos from Calculus Help (my teacher showed me the website and told me to use that).

8. chaise Group Title

Yes, that's correct. So you're differentiating using the definition? If you take the derivative of the equation y=3/(x^2-1) you can find the slope. if: f(x)=3/(x^2-1) then f(x+h)=3/((x+h)^2-1) dy/dx = (f(x+h)-f(x))/h Can you do the rest?

9. chaise Group Title

dy/dx =lim (h-->0) (f(x+h)-f(x))/h rather.

10. IsTim Group Title

Yes. That's what I did.

11. IsTim Group Title

But I can't go any further. |dw:1335262087563:dw| That's the furthest I got up to.

12. chaise Group Title

Expand your brackets and factor out a h.

13. IsTim Group Title

The bottom one to? I was told not too.

14. chaise Group Title

Not sure - I'm not familiar with the long method, I just use the shortcut :)

15. Callisto Group Title

Can you take derivatives? Must you use first principle to find it?

16. IsTim Group Title

Derivatives is our next unit.

17. IsTim Group Title

I can't isolate or factor out anything. I must had made a mistake beforehand I guess.

18. IsTim Group Title

Anyone?

19. Callisto Group Title

I hope you don't mind me posting my solution here

20. IsTim Group Title

I guess not, but it's notm much like my work.

21. Callisto Group Title

Oh shoot... I got some mistakes there! Wait

22. Callisto Group Title

Once again :(

23. Callisto Group Title

Oh my dear!!! The final answer should be -4/3 ... not -2 as I've written :S

24. Callisto Group Title

Is your question $\frac{3}{x^2-1}$ or $\frac{3}{x^2+1}$?

25. IsTim Group Title

First one.

26. IsTim Group Title

Maybe I should upload my work, and maybe you check for problems?

27. Callisto Group Title

Sure!

28. IsTim Group Title

IT's c.

29. IsTim Group Title

Starting from c) at Scan001.

30. Callisto Group Title

f(a) is not 1

31. Callisto Group Title

f(a) is 3/ (a^2 -1)

32. IsTim Group Title

but since x=2, I subbed in a=2 into that equation...

33. Callisto Group Title

for the denominator, (a+h)-a =h , not a+h -2 You need to find the limit before substituting the numbers.

34. Callisto Group Title

After you've found the limit, you'll see the unknown x. By then, sub x=2 and you'll get the slope. But NOT when you're taking the limit

35. IsTim Group Title

I thought the unknown to be m, and that h was still the variable withint the equation?

36. Callisto Group Title

h is something you need to deal with. Should I upload an example to should how you do first principle for you ?

37. IsTim Group Title

I've got an example here with me from my teacher.

38. Callisto Group Title

If you don't need it, it's okay :) Should I keep checking for you or you want to do corrections first?

39. IsTim Group Title

What should I correct?

40. Callisto Group Title

Correct starting from the third line For numerator: a -> 3/ (a^2 -1) For denominator: a+h-2 -> h (in your previous step, a+h -a, simplify it , you'll get h)

41. IsTim Group Title

Sorry if I sound ignorant, but that's how I saw it in the example...the h is alone.

42. Callisto Group Title

43. IsTim Group Title

44. Callisto Group Title

First, the situation is different . You're given 2 values there, but only 1 here. Second, to be frank, I don't understand what you (or your teacher) is doing. It's not the normal way as I've learnt.. Third, I still insist that you shouldn't sub the value immediately...

45. IsTim Group Title

Ok. I think I know what you are doing, and what my teacher is doing. You're going from a general formula, while my teacher is using the specific formula. The general formula doesn't sub in the x or a value until the end.

46. Callisto Group Title

It's good that you notice the difference :)

47. IsTim Group Title

Just looking through my notes I guess. I've got a test coming up, so I thought reviewing would be best.

48. Callisto Group Title

Yup :)

49. Mimi_x3 Group Title

well, where do you need help with? This is pretty long..

50. IsTim Group Title

Maybe I should just leave this question. I tried this for over 2 hours by now.

51. Mimi_x3 Group Title

First, what is the question? $\frac{1}{x-2}$?? or $\frac{3}{x^{2}-1}$??

52. IsTim Group Title

Second one, whereas x=2.

53. IsTim Group Title

Ok. Thanks for the attempt guys. I'll try other problems, and maybe this might make more sense.

54. Mimi_x3 Group Title

wait..i will try and do it first.. can't you take the derivative which is easier?

55. IsTim Group Title

Others suggested that, but that's for the next unit. I understand a bit on how that works, but I'm not allowed using it here.

56. Mimi_x3 Group Title

Hmm..I might try it but it might take a while since i havent done these in a while...

57. IsTim Group Title

Ok. Well, I guess you can do so, if yo uhave free time. But most likely you too have something important coming up (immediately).

58. Mimi_x3 Group Title

No, I don't have anything important..i might be able to do it but not sure..lol

59. Mimi_x3 Group Title

I have to review these anyway

60. apoorvk Group Title

^^That was mammoth. phew. Istim do you know how to differentiate using chain rule?

61. Mimi_x3 Group Title

lol, i failed...do you remember how to do these apoor? my brain is failling me :(

62. IsTim Group Title

No, I don't (Sorry, cleaning up house).

63. apoorvk Group Title

Hmm. so you want to do this by the first principle of finding derivatives okay.

64. IsTim Group Title

I am just oh so selective in the method used. That be the end of me.

65. Mimi_x3 Group Title

$\large\frac{f(x+h)-f(x)}{h} =>\frac{\frac{3}{(x+h)^{2}-1}-\frac{3}{x^{2}-1}}{h}$

66. Mimi_x3 Group Title

right so far?

67. IsTim Group Title

I have no idea.

68. chaise Group Title

should be the limit as h approaches zero, but, apart from that, correct. ^_^

69. Mimi_x3 Group Title

$\large =>\frac{\frac{3}{h^{2}+2hx+x^{2}-1}-\frac{3}{x^{2}-1}}{h}$ $\large >\frac{\frac{3(x^{2}-1)-3(h^{2}+2hx+x^{2}-1)}{(h^{2}+2hx+x^{2}-1)(x^{2}-1)}}{h}$

70. Mimi_x3 Group Title

I think that im doing it wrong..i dont think that its this complicated..

71. chaise Group Title

Perhaps you should just use quotient rule.

72. Mimi_x3 Group Title

but it says derivatiive thing is not allowed..

73. IsTim Group Title

Before using deratives. Referencing Calculus Phobe from Calculus Help. I think I used Conjugate Method.

74. Mimi_x3 Group Title

whaat..im lost..i looked at your example but it got confusing..then i looked at my book its more confusing..using the chain rule is easier.

75. Mimi_x3 Group Title

$\frac{3}{x^{2}-1} => 3(x^2-1)^{-1}$ $-3(x^2-1)^{-1}*2x$ $-6x(x^2-1)^{-1}$ easier i suppose..