Taylor polynomial

For example, if Mⁿ#61;#92;mathbb#123;R#125;ⁿ and Nᵏ#61;#92;mathbb#123;R#125;, a singularity means the vanishing of the gradient, or equivalently, the linear terms of the Taylor's p…

The polynomial approximation above for exp(x) is an example of a Taylor polynomial of degree 2 and in fact the polynomial approximations to sin(x) and cos(x) that we wrote down in…