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 ..

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- Nov 28th 2012, 10:18 AMclarkduncanlimit (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 .. - Nov 28th 2012, 11:38 PMhollywoodRe: limit (MVT)
I think the best method is to use Taylor's Theorem - it gives the expansion for $\displaystyle \cos{x}$ in powers of x as $\displaystyle 1-\frac{x^2}{2}$. The error term is $\displaystyle \frac{c^4}{24}$ where c is some number between x and 0. Since this error term is positive, $\displaystyle \cos{x}>1-\frac{x^2}{2}$ for all $\displaystyle x\ne{0}$.

- Hollywood