Taylor Polynomial (1 Viewer)

[tacogym27101990]

hey can someone please explain to me how to get a taylor polynomial of order two out of the equation x^2sqrt(9-x^2)
i missed a lecture where he explained it
i think it uses the fact that the expansion of sqrt(1+x) = 1 + 0.5x + ...
but dont know how to do it
thanks

 

[Iruka]

Presumably you are expanding around x=0?

sqrt(1+x) = 1+1/2*x-1/8*x^2+1/16*x^3-5/128*x^4+7/256*x^5+...

First, substitute in -9*x^2 where every you see an 'x' in the first series (this gives you the Taylor series for sqrt(1-9*x^2).

Then multiply every term by x^2. And truncate, to give you the desired polynomial.