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emcrazy14 Group Title

Urgent help needed: Expand the following up to the term in x^3:

  • 11 months ago
  • 11 months ago

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  1. emcrazy14 Group Title
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    \[\frac{ 1+x }{ \sqrt{1-x} }\]

    • 11 months ago
  2. Jibrilpresbury Group Title
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    idk

    • 11 months ago
  3. satellite73 Group Title
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    expand in a power series i take it

    • 11 months ago
  4. satellite73 Group Title
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    about zero i hope first term is \(f(0)=1\)

    • 11 months ago
  5. satellite73 Group Title
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    first derivative is \[f'(x)=\frac{3-x}{2\sqrt{1-x}^3}\] so second term is \[f'(0)x=\frac{3}{2}x\]

    • 11 months ago
  6. satellite73 Group Title
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    yikes, now we need the derivative of that beast

    • 11 months ago
  7. satellite73 Group Title
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    do i have to do that too?

    • 11 months ago
  8. emcrazy14 Group Title
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    Yes, please?

    • 11 months ago
  9. satellite73 Group Title
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    grrr

    • 11 months ago
  10. satellite73 Group Title
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    lets cheat

    • 11 months ago
  11. satellite73 Group Title
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    looks like it is \[f''(x)=\frac{7-x}{4\sqrt{1-x}^5}\]

    • 11 months ago
  12. satellite73 Group Title
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    making the next term \[\frac{f''(0)}{2}x^2=\frac{7}{8}x^2\]

    • 11 months ago
  13. satellite73 Group Title
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    one more?

    • 11 months ago
  14. emcrazy14 Group Title
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    So I find the derivative of that too?

    • 11 months ago
  15. satellite73 Group Title
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    \[f'^{(3)}(x)=\frac{33-3x}{8\sqrt{1-x}^7}\]

    • 11 months ago
  16. satellite73 Group Title
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    i think

    • 11 months ago
  17. satellite73 Group Title
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    if so then \(\frac{f^{(3)}(0)}{3!}x^3=\frac{33}{16}x^3\)

    • 11 months ago
  18. satellite73 Group Title
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    hmm let me check if this is right

    • 11 months ago
  19. satellite73 Group Title
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    no messed up \(3!=6\) doh

    • 11 months ago
  20. satellite73 Group Title
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    third term is \(\frac{11}{16}x^3\)

    • 11 months ago
  21. satellite73 Group Title
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    k lets check the whole dam thing and see if it is right

    • 11 months ago
  22. satellite73 Group Title
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    http://www.wolframalpha.com/input/?i=%281%2Bx%29%2Fsqrt%281-x%29 yup !!

    • 11 months ago
  23. emcrazy14 Group Title
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    Okay, thank you so much! :)

    • 11 months ago
  24. satellite73 Group Title
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    yw

    • 11 months ago
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