Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
at 0 to approxmate We will use the degree 4 Taylor polynomial for e -22 10.27 -² dz First enter in the degree 4 Taylor polynomial (hint: you don't need to calculate it with derivatives, you can use the Taylor series for e) P₁(e)- Now evaluate 0.27 P4 (2) dz to get the approximate value for the original integral, giving your answer accurate to 4 decimal places |数字 Note that the answer will most likely give a different answer to a calculator for the original integral, but it won't be too far off (the calculator is also using an approximation like this, but a better one). Let's try a bigger value. Use the same method to approximate 1.27 -2² dz 数字。 out that this approximation starts to significantly diverge from the function above

at 0 to approxmate We will use the degree 4 Taylor polynomial for e -22 10.27 -² dz First enter in the degree 4 Taylor polynomial (hint: you don't need to calculate it with derivatives, you can use the Taylor series for e) P₁(e)- Now evaluate 0.27 P4 (2) dz to get the approximate value for the original integral, giving your answer accurate to 4 decimal places |数字 Note that the answer will most likely give a different answer to a calculator for the original integral, but it won't be too far off (the calculator is also using an approximation like this, but a better one). Let's try a bigger value. Use the same method to approximate 1.27 -2² dz 数字。 out that this approximation starts to significantly diverge from the function above

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Please explain answer

We will use the degree 4 Taylor polynomial for eat z = 0 to approxmate 0.27 First enter in the degree 4 Taylor polynomial (hint: you don't need to calculate it with derivatives, you can use the Taylor series for e) P₁(z) = Now evaluate 0.27 P4 (2) dz to get the approximate value for the original integral, giving your answer accurate to 4 decimal places 数字 Note that the answer will most likely give a different answer to a calculator for the original integral, but it won't be too far off (the calculator is also using an approximation like this, but a better one). Let's try a bigger value. Use the same method to approximate 1-27-2² dz |数字 You should find now that it is is quite different to a calculator value. It turns out that this approximation starts to significantly diverge from the function above about = 0.6 and then goes badly wrong above = 1. You can see this for yourself if you plot them together on a graph. To get an approximation that works for larger a you need more terms from the Taylor Series. If you include enough torms you can get a good approximation of any at
Transcribed Image Text:We will use the degree 4 Taylor polynomial for eat z = 0 to approxmate 0.27 First enter in the degree 4 Taylor polynomial (hint: you don't need to calculate it with derivatives, you can use the Taylor series for e) P₁(z) = Now evaluate 0.27 P4 (2) dz to get the approximate value for the original integral, giving your answer accurate to 4 decimal places 数字 Note that the answer will most likely give a different answer to a calculator for the original integral, but it won't be too far off (the calculator is also using an approximation like this, but a better one). Let's try a bigger value. Use the same method to approximate 1-27-2² dz |数字 You should find now that it is is quite different to a calculator value. It turns out that this approximation starts to significantly diverge from the function above about = 0.6 and then goes badly wrong above = 1. You can see this for yourself if you plot them together on a graph. To get an approximation that works for larger a you need more terms from the Taylor Series. If you include enough torms you can get a good approximation of any at
Expert Solution
steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS