Maclaurin

TenSaru SG

The maclaurin expansion for 1/ sqroot(1-x²) = 1+ x²/2 + (3x^4)/8 +...

Question: Estimate the value for sqroot 3

i subbed x = sqroot (2/3) in the equation and got 1.5 but the answer scheme sub x=1/2 and then rearrange to get 256/147... I know the answer scheme's answer is way closer to the actual value than mine. Is there anything wrong with my method?

Thanks for helping!

wee_ws SG

Hi,

Your method is alright, except that it is not a good approximation as compared to x = 1/2.

Another possibility is to use the substitution x = -1/2.

As you may observe, many substitutions may be possible. What really matters is how close we can get to the true value.

Thanks.

Cheers,
Wen Shih