Chapter 3: Applications of Differentiation
Section 3.3: Taylor Polynomials
Example 3.3.4
At x=3, obtain the equation of the line tangent to the graph of fx=lnx2+3 x+2.
Solution
Initialize
Tools≻Load Package: Student Calculus 1
Loading Student:-Calculus1
Control-drag fx=… Context Panel: Assign Function
fx=lnx2+3 x+2→assign as functionf
Obtain the equation of the tangent line from the degree-1 Taylor polynomial
Type fx Context Panel: Tutors≻Taylor Approximation
fx→Taylor approximation tutor
Set Degree = 1
Set x=3
Figure 3.3.4(a) is an image of the Taylor Approximation tutor in which P1x, the Taylor polynomial of degree 1, determines the equation of the tangent line in the form y=P1x.
The tutor will appear with x=3 and the Degree set to the default 4.
Figure 3.3.4(a) Taylor Approximation tutor
Obtain the equation of the tangent line from first principles
Using the point-slope form, type the equation of the tangent line.
Press the Enter key.
y=f′3 x−3+f3
y=920⁢x−2720+ln⁡20
Of course, the degree-1 Taylor polynomial could also have been obtained from the Series option in the Context Panel.
<< Previous Example Section 3.3 Next Section >>
© Maplesoft, a division of Waterloo Maple Inc., 2024. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
For more information on Maplesoft products and services, visit www.maplesoft.com
Download Help Document