Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

soobinkiki

  • 2 years ago

I NEED HELP.. Taylor series for x^2e^x and expanded around the point a=1/2

  • This Question is Closed
  1. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hi

  2. RolyPoly
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Let f(x) = x^2 e^x \[f(x) = f(a) + f'(a) (x-a) + \frac{f''(a)}{2!}(x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+... +\frac{f^{(n)}(a)}{n!}(x-a)^{n} +...\] So, you need to keep differentiating f(x)... Reference: http://mathworld.wolfram.com/TaylorSeries.html

  3. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok i will work on it and i will put what i did

  4. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is f ' (x) = 2xe^x?

  5. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hello

  6. RolyPoly
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[f'(x) = e^x \frac{d}{dx}(x^2) + x^2\frac{d}{dx}(e^x)\]

  7. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh product rule

  8. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how many time do i have to do differentiation? (how do i know?)

  9. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    are you there? please help me

  10. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hi

  11. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what i have done so far is

  12. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i took differentiation of f(x)=x^2e^x

  13. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so i got f '(x)=x^2e^x+2xe^x f ''(x)=4xe^x+x^2e^x+2e^x

  14. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and i know that taylor series formula f(x)=f(a)+f'(a)(x-a)+ - - - what don't know what to do next..

  15. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    my a = 1/2

  16. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    should i just plug in everything on the formula?

  17. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so my f(a) should be 1/4e^1/2 ??

  18. RolyPoly
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    f(a) is right. Check this: http://www.wolframalpha.com/input/?i=+Taylor+series+x%5E2e%5Ex+at+x%3D1%2F2 It's not something nice

  19. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you RolyPoly but last quick question

  20. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how do i know how many times should i take differentiation of f(x)?

  21. RolyPoly
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Actually, I don't know too...

  22. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    LOLLLLLL ok! RolyPoly anyways thank you so much!

  23. genius12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Is that (x^2)*(e^x)? @soobinkiki

  24. RolyPoly
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[f'(x) = 2xe^x+x^2e^x\]\[f''(x)=2(e^x+xe^x) + 2xe^x+x^2e^x=e^x(2+4x+x^2)\]\[f''(\frac{1}{2})=e^{\frac{1}{2}}(2+4(\frac{1}{2})+(\frac{1}{2})^2)=\sqrt{e}(2+2+\frac{1}{4}) = \frac{17}{4}\]

  25. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hey rolypoly can you click the website that you sent me?

  26. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it says f''(1/2) is 17/8(e^1/2)

  27. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that's why i was confused..

  28. RolyPoly
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The second term is \[\frac{f''(a)}{2!}(x-a)^2\]So, it is \[\frac{\frac{17}{4}\sqrt{e}}{2!}(x-a)^2\]that is \[\frac{17}{8}(x-a)^2\]

  29. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    shoot...... how i missed that....

  30. RolyPoly
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[=\frac{\frac{17}{4}\sqrt{e}}{2!}(x-\frac{1}{2})^2\]\[=\frac{17}{8}\sqrt{e}(x-\frac{1}{2})^2\]

  31. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i got it now ! thanks a lot!

  32. soobinkiki
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and the series of this problem is pretty long.......................

  33. genius12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Obviously it's long, it's a series with infinite terms.. -.-

  34. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.