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

needhelp07 Group Title

Problem : Find the derivatives of the function using the limit of definition y=x^4

  • one year ago
  • one year ago

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

    still the same type of question? try going http://www.math.hmc.edu/calculus/tutorials/limit_definition/ they show you examples. just apply your question to how they solve it.

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

    It cant be that you were taught 2 other similar questions but still cant solve it.

    • one year ago
  3. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    im confused about the exponent 4

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

    do you know how to do (a+b)^4?

    • one year ago
  5. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    no

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

    its the binomial theorem or pascal triangle

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

    1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 etc....

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

    for example just look at the pascal triangle for the coefficients (a+b)^2= 1a^2 + 2ab +1b^2= a^2 +2ab+b^2 can you guess whats (a+b)^3? and for (a+b)^4?

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

    note it can be like (x+y)^3 ? or (x+y)^4 ?

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

    so power of 3 we get the coefficients of 1 3 3 1 therefore the answer for (x+y)^3= x^3 +3x^2y +3 xy^2 + y^3 can you guess for (x+y)^4 ?

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

    the reason i want you to learn this is when you go solved for the derivative of y=x^4 you will get to find (x+y)^4

    • one year ago
  12. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    tnx a lot . i need to study more about this

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

    im here now to teach you the easier way of doing it

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

    ok for the power of 4 the coefficents inthe pascal triangle are 1 4 6 4 1 therefore (a+b)^4 = a^4 + 4a^3 b +6 a^2 b^2 +4 a b^3 + b^4 or (x+y)^4= x^4 +4x^3 y + 6 x^2 y^2 + 4x y^3 + y^4 did you see it ?

    • one year ago
  15. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

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

    now for practice y=x^2 \[y+\Delta y=x +\Delta x\] \[\Delta y=x+\Delta x - y\] \[\Delta y= (x+\Delta x)^{2}-x ^{2}\]

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

    can you try solving that first ?

    • one year ago
  18. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    wait

    • one year ago
  19. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i try solving it

    • one year ago
  20. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the answer is 2x

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

    \[\Delta y=f(x+\Delta x) - y\] \[\Delta y=(x+\Delta x)^{2}- x ^{2}\] \[\Delta y= x ^{2 }+ 2x \Delta x +\Delta x ^{2} -x ^{2}\] add or subtract we get \[\Delta y= 2x \Delta x+\Delta x ^{2}\] now the derivative is \[y'=f'(x)= \lim _{\Delta x ->0}\frac{ \Delta y }{ \Delta x }=\] \[= \lim _{\Delta x->0}(\frac{ 2x \Delta x+\Delta x ^{2} }{ \Delta x })\] try to cancell something in there

    • one year ago
  22. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i know it already the answer is 2x

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

    ok good can you try it if its y=x^4 ? do the same process

    • one year ago
  24. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    okay

    • one year ago
  25. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the answer is 4x^3+6x^2+4x

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

    hmm to make it easier lets make delta x=h so that delta y=(x+h)^4 - x^4 try solving that first

    • one year ago
  27. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I cant follow my professor's teaching. Good to know that u are here to help me .thank you so much. you are a great help! i need to do more assignments about this so i will go out now .

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

    the answer should be f'(x)=4x^3

    • one year ago
  29. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    haha im wrong

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

    do the process i gave you there, and you will arrive at the correct answer ... :D

    • one year ago
  31. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i wish i have a tutor like u hahaha .

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

    remember this ?. (x+y)^4= x^4 +4x^3 y + 6 x^2 y^2 + 4x y^3 + y^4 make y an h here so that (x+h)^4= x^4 +4x^3 h + 6 x^2 h^2 + 4x h^3 + h^4

    • one year ago
  33. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    anyway thx a lot

    • one year ago
  34. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    goodbye!

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

    ok just read it through here again and learn from it good luck and have fun now :D

    • one year ago
  36. needhelp07 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

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

    ok just messege me here and if you have prob i will go and give you an advise or correct if you have something done incorrectly ... :D

    • 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.