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• 1 Post By hollywood

# Thread:

1. ## limit (MVT)

show that Show that cosx>1-(x²/2) "x>0 o "x<0
hint:for x>0, you can use Mean value theorem for f(x)=cosx+(x²/2) on [0,x]

Thank you ..

2. ## Re: limit (MVT)

I think the best method is to use Taylor's Theorem - it gives the expansion for $\cos{x}$ in powers of x as $1-\frac{x^2}{2}$. The error term is $\frac{c^4}{24}$ where c is some number between x and 0. Since this error term is positive, $\cos{x}>1-\frac{x^2}{2}$ for all $x\ne{0}$.

- Hollywood
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