Hi everybody,

I must show that there exists a function f defined on $\displaystyle [-1,+\infty[$ such as :

$\displaystyle \{{(\forall x \in [-1,+\infty[) \sqrt{1+x}=1+\frac{1}{2}x-\frac{1}{8}x^2+x^2\phi(x)\atop\lim_{x\to 0} \phi(x)=0}$

I don't know what to do, can you help me please.

And thank you anyway.