A- The goal of this part is to find an approximate value of In(1.1) by using the Taylor expansion. We consider the function f(t) = In(1 + t). Show by induction on n that, the nth derivative of f is given by: /() = (-1)^-1 (n – 1)! (1+t)" Write the nh Taylor expansion of f at a=0 with the remainder R.. Show that max f+)(t)| = n! tel0,0.1] 10-(+1) when r 0.1. Deduce that |RIS Deduce how many terms in Taylor expansion of f at a =0 do we need to approximate f(0.1) In(1.1) within 6 decimale places. The goal of this part is the calculation of limits of functions by using the Taylor expansion. By atilizing the MacLaurin-Young formula of order 2 of cos z and sin r determine the limits n+1 I sinz - lim -40 2-2 cos z COs z e- lim Z-40
A- The goal of this part is to find an approximate value of In(1.1) by using the Taylor expansion. We consider the function f(t) = In(1 + t). Show by induction on n that, the nth derivative of f is given by: /() = (-1)^-1 (n – 1)! (1+t)" Write the nh Taylor expansion of f at a=0 with the remainder R.. Show that max f+)(t)| = n! tel0,0.1] 10-(+1) when r 0.1. Deduce that |RIS Deduce how many terms in Taylor expansion of f at a =0 do we need to approximate f(0.1) In(1.1) within 6 decimale places. The goal of this part is the calculation of limits of functions by using the Taylor expansion. By atilizing the MacLaurin-Young formula of order 2 of cos z and sin r determine the limits n+1 I sinz - lim -40 2-2 cos z COs z e- lim Z-40
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,