Question

The absolute value of which of the following is smaller with E being very very small number greater than zero?
a. [(4-E/2)^1/2]-2
b.[(4+E/2)^1/2]-2

I know the answer is b, but how do you figure it out without using a calculator?

Answer 1

right, but your getting that the absolute values are the same. I need to know which absolute value is smaller

Answer 2

re-reading it, The absolute value is the distance from 0, so we need 3 terms
\[ \sqrt{1 \pm x} \approx 1 \pm \frac{x}{2} - \frac{x^2}{8} ....\]

for 1+x we will get +x/2 - x^2/8
for 1-x -x/2 - x^2/8
the 2nd will have a slightly larger absolute value

Answer 3

Got it, thank you :)