how do I use this equation for this taylor series

[calcnoob145]

here is my problem


and i'm suppose to use the sqrt(1+x) equation with the equation given

the numbers on the left are the first four terms of the series but I'm having a difficult time rearranging the original equation so I can use the sqrt(1+x) and just substitute in numbers rather than differentiating the original term

 

[DrPhil]

here is my problem
View attachment 2780

and i'm suppose to use the sqrt(1+x) equation with the equation given

the numbers on the left are the first four terms of the series but I'm having a difficult time rearranging the original equation so I can use the sqrt(1+x) and just substitute in numbers rather than differentiating the original term

GIVEN: \(\displaystyle \sqrt{1 + x} = 1 + \dfrac{x}{2} - \dfrac{x^2}{8} + \dfrac{x^3}{16} - \cdot \cdot \cdot \)

FIND: \(\displaystyle \sqrt{9 - 63x^2} = 3 \sqrt{1 - 7 x^2} \)

Replace x with -7x^2:

\(\displaystyle \sqrt{1 + (-7x^2)} = 1 + \dfrac{(-7x^2)}{2} - \dfrac{(-7x^2)^2}{8} + \dfrac{(-7x^2)^3}{16} - \cdot \cdot \cdot \)

Expand the powers of (-7x^2), and collect like powers of x.

OK?

 

[calcnoob145]

oh ok thank you so much