Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

burhan101 Group Title

limit

  • one year ago
  • one year ago

  • This Question is Closed
  1. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1350454227197:dw|

    • one year ago
  2. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1350454341729:dw|

    • one year ago
  3. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Lol, derivative?

    • one year ago
  4. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes i think so that doesnt cancel out tho -.- im making a mistake

    • one year ago
  5. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge \lim_{h \rightarrow 0}\frac{[(x+h)^{3}-3]-(x^{3}-3)}{h}\] is this it?

    • one year ago
  6. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yupp ! how do you make it big like that btw ?

    • one year ago
  7. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    uhh, before typing in your equations and stuff, put in \huge

    • one year ago
  8. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks:D

    • one year ago
  9. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    This looks like you're taking the derivative of \[\huge x^{3} - 3\]

    • one year ago
  10. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yup that's right !

    • one year ago
  11. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    And you're to get the derivative using limits? lol, that's harsh... :D

    • one year ago
  12. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yess i have to

    • one year ago
  13. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You'll realise soon that there are faster ways of getting the derivative... anyway, just evaluate the numerator and show me what you get...

    • one year ago
  14. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    x^3 's cancel 3's cancel... what's left?

    • one year ago
  15. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    3x^2h + 3xh^2 +h^3 all divided by h factor out an 'h' in the numerator cancel with the 'h' in the denom. now you can take the limit without issues.

    • one year ago
  16. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\huge \ \frac{ x^3+3x^2h+3xh^2-3-x^2+3 }{h }\]

    • one year ago
  17. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    no.

    • one year ago
  18. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i have an x^3 and x^2 ? :S

    • one year ago
  19. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    no.

    • one year ago
  20. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Well that changes everything...

    • one year ago
  21. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{ f(x+h) - f(x) }{h }\]

    • one year ago
  22. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    what's f(x)?

    • one year ago
  23. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    x^3 -3

    • one year ago
  24. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{(x+h)^3 -3 - ( x^3 -3) }{h }\]

    • one year ago
  25. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    no f(x)=x^2-3

    • one year ago
  26. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thats why it doesnt cancel out

    • one year ago
  27. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    you expanded correctly: \[\frac{ x^3 +3x^2h +3xh^2 +h^3 -3 - (x^3 -3) }{h }\]

    • one year ago
  28. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

    • one year ago
  29. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    then why are you cubing (x+h) ?

    • one year ago
  30. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhh i should square it *facepalm*

    • one year ago
  31. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{ (x+h)^2 -3 -(x^2-3) }{h }\]

    • one year ago
  32. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    can you help me with this one: find the equation of the tangent \[y=\frac{ x-2 }{ x+2 }\] when x=0

    • one year ago
  33. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\huge \lim_{h \rightarrow 0} \frac{ (x+h)-2 }{ (x+h)+2 } -\frac{ x-2 }{ x+2 }\]

    • one year ago
  34. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @terenzreignz

    • one year ago
  35. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Equation of the tangent involves derivatives, right?

    • one year ago
  36. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

    • one year ago
  37. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Quotient rule? Ever dabbled with it?

    • one year ago
  38. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    no we're not allowed to use that yet -.-

    • one year ago
  39. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Here, I don't think I have the attention span to type this out o.O http://www.math.hmc.edu/calculus/tutorials/quotient_rule/proof.pdf

    • one year ago
  40. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You're allowed to use anything as long as you can prove it ;)

    • one year ago
  41. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    my tests always state "Only using method thought in class" i know that quotient rule is so much faster

    • one year ago
  42. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and we we're never thought that in class yet

    • one year ago
  43. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, don't despair :D I'll see what I can do... To get the equation of the tangent line, first we need a slope. to get that slope, we need the derivative. So what's the derivative (go ahead and express it first in limit-form)

    • one year ago
  44. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\huge \lim_{h \rightarrow o}\frac{ (x+h)-2 }{ (x+h)+2 } - \frac{ x-2 }{ x+2 }\]

    • one year ago
  45. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    nope... you forgot that all that must also be divided by h... small details, but no less important...

    • one year ago
  46. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ohh i did :$

    • one year ago
  47. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    tsk \[\huge \lim_{h \rightarrow 0}\frac{\frac{ (x+h)-2 }{ (x+h)+2 } - \frac{ x-2 }{ x+2 }}{h}\]

    • one year ago
  48. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok yupp

    • one year ago
  49. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Right, well this can also be written as \[\lim_{h \rightarrow 0}\frac{1}{h}\left( \frac{ (x+h)-2 }{ (x+h)+2 } - \frac{ x-2 }{ x+2 } \right)\]

    • one year ago
  50. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh okayy

    • one year ago
  51. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    now \[\lim_{h \rightarrow 0}\frac{1}{h}\frac{\left[ \left( x+h \right)-2 \right]\left( x+2 \right)-\left[ \left( x+h \right)+2 \right]\left( x-2 \right)}{\left[ \left( x+h \right)+2 \right]\left( x+2 \right)}\] o.O

    • one year ago
  52. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    wait, how did you get rid of those fractions ?

    • one year ago
  53. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Like magic :P \[\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}\]

    • one year ago
  54. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Get it now?

    • one year ago
  55. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yeaaah ! i do

    • one year ago
  56. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and then cancelling

    • one year ago
  57. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Hey, there's nothing you can cancel...

    • one year ago
  58. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    then expansion and cancelling out the like terms

    • one year ago
  59. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Nothing that would you do you much good, anyway... Here's a tricky bit of manipulation \[\lim_{h \rightarrow 0}\frac{1}{h}\frac{\left[ \left( x+h \right)-2 \right]\left( x+2 \right)-(x-2)(x+2)+(x-2)(x+2)-\left[ \left( x+h \right)+2 \right]\left( x-2 \right)}{\left[ \left( x+h \right)+2 \right]\left( x+2 \right)}\]

    • one year ago
  60. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    wow o.O

    • one year ago
  61. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    All right, scratch everything, I overlooked one important detail...

    • one year ago
  62. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You only need to get its slope on the specific case where x = 0 right?

    • one year ago
  63. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Use this definition of derivative instead: \[f'(c)=\lim_{x \rightarrow c}\frac{f(x)-f(c)}{x-c}\]

    • one year ago
  64. burhan101 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    whats c ?

    • one year ago
  65. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Sorry for this extremely late reply, I was busy with something :( c is 0.

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.