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Math Help - squareroot (1 + ...) , log (1 + ...)

  1. #1
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    squareroot (1 + ...) , log (1 + ...)

    Since I suspect that both cases have a similar apoach I combine these two.
    According to an exercise-exam of my university \sqrt{1+(1/x^2)} is aproximately equal to 1 + (1/2x^2) and log{(1 + (1/4x^2))} aproximately equal to 1/(4x^2)

    Why?
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  2. #2
    Super Member Matt Westwood's Avatar
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    1. Expand using the binomial theorem and take the first non-trivial term.

    2. Use a Taylor expansion, same thing.
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