Chapter 9.2, Problem 34E

To determine

To explain: The connection between the linearization of f and Taylor series.

Answer to Problem 34E

The first order Taylor series is linearization of function.

Explanation of Solution

• The Taylor series is a n^th polynomial series. It is a series expansion of any function. It can be shown as:

$\begin{array}{l}$ f(x)=f(x_0)+f\text{'}(x_o)(x-x_0)+\frac{f"(x_0)}{2!}{(x-x_0)}^2+\mathrm{........}$f(x)={\displaystyle \sum _{n=0}^{\infty }\frac{f^{(n)}(x_0)}{n!}{(x-x_0)}^n}\end{array}$

• The first order polynomial is known as linearization of function. So, this is the relation between them that linearization of function is basically a first order Taylor series.
• So, when $f(1)$ is calculated then, Taylor series is known as linearization of function.

Conclusion:

The first order Taylor series is linearization of function.