Use a binomial of the 6th degree to approximate: 1/sqrt(1-x^2)

FightingEmu said:

Use a binomial of the 6th degree to approximate:

1/sqrt(1-x^2)

I factored out a -x^2 to get ........ You cannot do that (i.e. factoring out a negative number from a square-root)


1/(1+x)^(1/2)

I then used the k/n! rule to expand the binomial and got

1+2/x^2-8/x^2+16/x^3

Finally, I replaced the -x^2

1-2/x^2-8/x^4-16/x^6

This, nor any simplification of, is the correct answer according to the program that grades homework.
I know I'm supposed to somehow manipulate the problem to terms of (1+x)^k and work from there. The
homework also says 1/sqrt(1-x^2) is equal to arcsin(x), if that helps
Where did I go wrong?

Click to expand...

FightingEmu said:

Use a binomial of the 6th degree to approximate:

1/sqrt(1-x^2)

I factored out a -x^2 to get

1/(1+x)^(1/2)

I then used the k/n! rule to expand the binomial and got

1+2/x^2-8/x^2+16/x^3

Finally, I replaced the -x^2

1-2/x^2-8/x^4-16/x^6

This, nor any simplification of, is the correct answer according to the program that grades homework.
I know I'm supposed to somehow manipulate the problem to terms of (1+x)^k and work from there. The
homework also says 1/sqrt(1-x^2) is equal to arcsin(x), if that helps
Where did I go wrong?

Click to expand...