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

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• Aug 11th 2009, 01:26 PM
Sebastian de Vries
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?
• Aug 11th 2009, 01:50 PM
Matt Westwood
1. Expand using the binomial theorem and take the first non-trivial term.

2. Use a Taylor expansion, same thing.