# 1. Find the second-degree Taylor polynomial T_2(x) for the function f(x) = 3 + x^2 at the...

## Question:

1. Find the second-degree Taylor polynomial{eq}\displaystyle \ T_2(x) {/eq} for the function{eq}\displaystyle \ f(x) = \sqrt {3 + x^2} {/eq} at the number{eq}\displaystyle \ x = 1. {/eq}

2. Find the second-degree Taylor polynomial for{eq}\displaystyle \ f(x) = 4x^2 - 9x + 1 {/eq} about{eq}\displaystyle \ x = 0. {/eq} What do you notice about your polynomial?

## Taylor Polynomial:

The second degree Taylor polynomial of a function {eq}f(x) {/eq} at a point {eq}x_0 {/eq} can be evaluated by using the following formula

{eq}T_2(x) = f(x_0) + f'(x_0)(x-x_0) + \frac{1}{2}f''(x_0)(x-x_0)^2 {/eq}

The second order Taylor polynomial of the function

{eq}f(x) = 3 + x^2 {/eq}

at point x=1.2 is found as

{eq}f'(x) = 2x \\ f''(x) = 2 \\ f(1.2) =...

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Taylor Series, Coefficients & Polynomials: Definition, Equations & Examples

from GRE Math: Study Guide & Test Prep

Chapter 12 / Lesson 8
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