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    Hi,

    I'd appreciate it if someone could solve this limits problem for me. I know I can easily do it using Hópitals Rule but I just want to do it using the Taylor Polynomials shown. I think it's quite a simple question but for some reason my brain is freezing!

    Thanks in advance!
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    \cosh(x)-\cos(x) = 1+\frac{1}{2}x^{2} + \frac{1}{24}x^{4} - 1 + \frac{1}{2}x^{2} - \frac{1}{24}x^{4} + O(x^{6}) = x^{2} + O(x^{6})
    Therefore
    \frac{\cosh(x)-cos(x)}{x^{2}} = \frac{x^{2}+O(x^{6})}{x^{2}} = 1 + O(x^{4})

    As x->0, O(x^{4}) \to 0 so the limit is 1.
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    Thanks dude! I did it using Hopitals rule and got 1, then for some reason my basic algebra knowledge went out of the window!

    Ta again!
 
 
 
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Updated: November 22, 2005

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