List of Notes - Category: Taylor Formula

Taylor Polynomial

Suppose that we have n-th degree polynomial `p(x)=a_0+a_1(x-a)+a_2(x-a)^2+...+a_(n-1)(x-a)^(n-1)+a_n(x-a)^n`, where `a,a_0,a_1,a_2,...,a_n` are constants.

Now, differentiate this polynomial `n` times:

Maclaurin Polynomials of Common Functions

When `a=0` we call Taylor polynomial Maclaurin polynomial. In this case formulas for polynomials are fairly simple.

Maclaurin Polynomial. For function `y=f(x)` Maclaurin polynomial of n-th degree is `M_n(x)=f(0)+(f'(0))/(1!)x+(f''(0))/(2!)x^2+...+(f^((n))(0))/(n!)x^n`.