1. ## loss of significance

Loss of significance errors can be avoided by rearranging the function being evaluated. I must rearrange these functions to avoid loss of sig.

a) f(x) = (1-cosx)/x^2

b) f(x) = (cube root (1+x)) - 1

I havn't a clue... any advice?

Thanks for any help.

2. Originally Posted by jzellt
Loss of significance errors can be avoided by rearranging the function being evaluated. I must rearrange these functions to avoid loss of sig.

a) f(x) = (1-cosx)/x^2

b) f(x) = (cube root (1+x)) - 1

I havn't a clue... any advice?

Thanks for any help.
I'll do (a).

Loss of significance occurs at $x=0$. Note that $\frac{1-\cos x}{x^2}=\frac{1-\cos x}{x^2}\cdot\frac{1+\cos x}{1+\cos x}=\frac{1-\cos^2 x}{x^2\left(1+\cos x\right)}=\left(\frac{\sin x}{x}\right)^2\cdot\frac{1}{1+\cos x}$.

Now note that as $x\to 0$, $\frac{\sin x}{x}\to 1$. Thus, $\left(\frac{\sin x}{x}\right)^2\cdot\frac{1}{1+\cos x}\sim \frac{1}{1+\cos x}$.

3. Thanks, but how do you know to multiply by 1 + cosx / 1 + cosx?

For the second question, would I multiply by (cube root(1-x)) / cube root(1-x))?