Taylor Polynomials

Description

The $n$-degree Taylor polynomial of a function $f(x)$ at a point $x = x_0$ is defined as

(1)
\begin{align} T_n(x) = f(x_0) + f'(x_0)(x - x_0) + \frac{f''(x_0)}{2!}(x - x_0)^2 + \cdots + \frac{f^{(n)}(x_0)}{n!}(x - x_0)^n. \end{align}

We can use Sage to compute Taylor polynomials. As an example, we can compute the 8-th degree Taylor polynomial of $f(x) = \cos x$ at the point $x_0 = 0$.

Sage Cell

Code

f(x) = cos(x)
T(x) = taylor( f(x), x, 0, 8 )
T


None

Tags

Primary Tags: Calculus - Single Variable

Secondary Tags: Infinite Sequences and Series: Taylor Series

Related Cells

Related cells: None