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Homework Help: Fill in the blank help

  1. May 8, 2006 #1
    These two problems are a big pain (never worked a problem in this format before). # represents a number that needs to be plugged into the problem to equal the given number. All #'s are the same when you find them so in problem 1 the 4 unknown #s are not different. #=#

    1.
    # + 4*#^2+9*#^3+16*#^4.... =6

    i re wrote it so it looks like this # +2^2 * #^2 + 3^2 * #^3 = 4^2 * #^4
    Looks like a taylor series. Series of 1 over 1-x? but how do i apply that?



    2.
    lim (1+#x)^#/x = 4
    x-0

    for 2 i was really confused. I was thinking of appyling the natrual log so i would get ln #/x (1+#x) and apply L'Hopital's rule to that but i dont think thats the correct method.

    Sorry im just really confused because I never worked problems like these (fill in the blank) before. Any help would be apperciated.
     
  2. jcsd
  3. May 8, 2006 #2

    Tide

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    Science Advisor
    Homework Helper

    HINT: If

    [tex]f(x) = \frac {1}{1-x}[/tex]

    then

    [tex]\frac {d}{dx} \left( x \frac {df}{dx} \right) = 1 + 2x + 9x^2 + \cdot \cdot \cdot [/tex]
     
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