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    Getting n alone in n!=x and nlgn=x

    Homework Statement I need to know the greatest n for which n! is greater or equal to x, and the greatest n for which nlgn is greater or equal to x. Homework Equations Can't think of any. Sorry! The Attempt at a Solution For a "normal" function, like, say, lgn or n^2, it would be...
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    McLaurin - when do you stop?

    Homework Statement I have a problem with McLaurin series. I never know when to stop. How do I know if O(x3) is adequate, or O(x5)? Let's take this exam question as an example. \lim_{x \to 0} \frac{(x+1)e^x -1-2x}{cosx-1} \frac{(x+1)e^x -1-2x}{cosx-1} = \frac{(x+1)(1+x+\frac{x^2}{2!}+...)...
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    D/dx |x+2|^x (solution known, need explanation)

    Cyosis - got it, thanks! g_edgar - I agree, but the example was taken from an old exam and what I wrote in the first post was the only answer or explanation given in the solutions. I don't know if a solution taking two cases would have given full credit.
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    D/dx |x+2|^x (solution known, need explanation)

    Ok, yes, you're right. Thanks! Not that it matters that much to me right now, but how is it a consequence of the chain rule?
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    D/dx |x+2|^x (solution known, need explanation)

    Hm. \frac{d}{dx} e^x = e^x \frac{d}{dx} x and \frac{d}{dx} ln|x| = \frac{1}{x} so \frac{d}{dx} e^{x \log|x+2|} = e^{x \log|x+2|} \frac{d}{dx}(x \log|x+2|) = e^{x \log|x+2|} (ln|x+2| + \frac{x}{x+2}) = |x+2|^x (ln|x+2| + \frac{x}{x+2}) Thanks for the tip, I would never have thought of...
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    D/dx |x+2|^x (solution known, need explanation)

    Solved! d/dx |x+2|^x Homework Statement I need someone to explain this: http://www.dafydd.se/stuff/solvethis.png [Broken] Homework Equations I guess the following are of relevance... \frac{d}{dx} |x| = \frac{x}{|x|} \frac{d}{dx} a^x = a^x ln a The Attempt at a Solution The...
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