Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Find the truncuation error of the maclaurin series sinx cosx given that is truncated into three terms.

Find the truncuation error of the maclaurin series sinx cosx given that is truncated into three terms.

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

Find the truncuation error of the maclaurin series sinx cosx given that is truncated into three terms.

See the example below...

 

9:45 M < 03_Handout_2-2 Save -x³ + ·… 120 Since the above equation is truncated into 3, thus, e* = 1+x + x? 2. Step 1: f(x) = cos x: Calculate the derivatives for the function Step 2: Fill in the derivatives you calculated in step 1 with 0 as the input. This gives you the values you need f(x) = cos x to insert into the Maclaurin series: f'(x) = (cos x) = – sin x dx d? (cos x) = – cos x f(x) = cos(0) = 1 f'(0) = – sin(0) = 0 f"(0) = – cos(0) = –1 f"(x) = dx2 03 Handout 2 *Property of STI Page 3 of 4 STI IT1903 f''0) = sin(0) = 0 f"(0) = cos(0) = 1 f'(0) = – sin(0) = 0 f''(x) = - dx3 (cos x) = sin x f"(x) (cos x) = cos x dx4 d5 f'(x) = dr5 (cos x) = – sin x Step 3: Fill in the Maclaurin formula with the values you calculated in Step 2: Solution: Truncation Error = Actual Value Truncated Value cos X %3D 1+ 유(x) + 뮤(x)2 + 을(x)3 + Truncation Error = (1- ;x² + -x4 24 Truncation Error = .. cos x = 1+ (0) + x2 + x³ + x* + (0) x5 120 + ... 1 cos x = 1 – x² +x*. Since the above equation is truncated into 3, thus, cos x = 1 – *Property of STI Page 4 of 4 03 Handout 2 II
Transcribed Image Text:9:45 M < 03_Handout_2-2 Save -x³ + ·… 120 Since the above equation is truncated into 3, thus, e* = 1+x + x? 2. Step 1: f(x) = cos x: Calculate the derivatives for the function Step 2: Fill in the derivatives you calculated in step 1 with 0 as the input. This gives you the values you need f(x) = cos x to insert into the Maclaurin series: f'(x) = (cos x) = – sin x dx d? (cos x) = – cos x f(x) = cos(0) = 1 f'(0) = – sin(0) = 0 f"(0) = – cos(0) = –1 f"(x) = dx2 03 Handout 2 *Property of STI Page 3 of 4 STI IT1903 f''0) = sin(0) = 0 f"(0) = cos(0) = 1 f'(0) = – sin(0) = 0 f''(x) = - dx3 (cos x) = sin x f"(x) (cos x) = cos x dx4 d5 f'(x) = dr5 (cos x) = – sin x Step 3: Fill in the Maclaurin formula with the values you calculated in Step 2: Solution: Truncation Error = Actual Value Truncated Value cos X %3D 1+ 유(x) + 뮤(x)2 + 을(x)3 + Truncation Error = (1- ;x² + -x4 24 Truncation Error = .. cos x = 1+ (0) + x2 + x³ + x* + (0) x5 120 + ... 1 cos x = 1 – x² +x*. Since the above equation is truncated into 3, thus, cos x = 1 – *Property of STI Page 4 of 4 03 Handout 2 II
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

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