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Find the Taylor polynomial of degree $n$ centered at the number $a$.$f(x)=\sqrt{x}, \quad n=2, \quad a=4$

$T_{2}(x)=f(a)+f^{\prime}(a)(x-a)+f^{\prime \prime}(a) \frac{(x-a)^{2}}{2 !}=2+\frac{1}{4}(x-4)-\frac{1}{64}(x-4)^{2}$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:40

In mathematics, a derivati…

30:01

In mathematics, the deriva…

01:16

Find the Taylor polynomial…

02:04

01:06

Finding a Taylor Polynomia…

04:53

In the following exercises…

08:44

02:02

02:42

01:50

06:24

a. Find the nth-order Tayl…

02:16

Use a computer algebra sys…

09:47

09:57

06:38

02:23

10:57

03:00

03:18

11:18

Graph $f(x)$ and the Taylo…

05:51

Find the remainder term $R…

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