# limit (MVT)

• November 28th 2012, 10:18 AM
clarkduncan
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 ..
• November 28th 2012, 11:38 PM
hollywood
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