binomial expansion

[trail ember]

<@&791435371564892232> for part b, how do we know the domain for when the expansion is valid and which value would lead to the most accurate approximation?

[raven chasm]

substituting x=0 into the equation gives us 1/2, so using 1/2 will give the most accurate approximation of sqrt2

using -14 shld give the least accurate approximation i think, as its the largest value and is 6 times smaller than sqrt2

[spark moat]

?

It says from those 3 values

The expansion is valid for |x| < 4

Sp definitely not -14

Root 2/ 3 would mean making it smaller than root2/2

Because u r dividing by a bigger number

So ig the best one would be x =2

[raven chasm]

ye that's the reason for first

mb

but the second part, the value closest to 0 gives the most accurate approximation iirc

i thought it would be 2 aswell but 1/2 is less

[spark moat]

It's asking for which one of those three values tho