Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
== 3.14. Prove l'Hôpital's rule in the following form. Suppose f(a) = f'(a) = f(n-1) (a) = 0, g(a) = g'(a) = == g(n-¹)(a) = 0, and either f(n) (a) #0 or g(n) (a) #0 (or both); then f(x) lim x-a g(x) 8 f(n) (a) g(n)(a) if g(n) (a) = 0, otherwise. (Suggestion: Use Taylor's formula with Lagrange's form of the remainder, for both f(a+Ax) and g(a + Ax).)

== 3.14. Prove l'Hôpital's rule in the following form. Suppose f(a) = f'(a) = f(n-1) (a) = 0, g(a) = g'(a) = == g(n-¹)(a) = 0, and either f(n) (a) #0 or g(n) (a) #0 (or both); then f(x) lim x-a g(x) 8 f(n) (a) g(n)(a) if g(n) (a) = 0, otherwise. (Suggestion: Use Taylor's formula with Lagrange's form of the remainder, for both f(a+Ax) and g(a + Ax).)

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
== 3.14. Prove l'Hôpital's rule in the following form. Suppose f(a) = f'(a) = .. f(n-1)(a) = 0, g(a) = g'(a) = ... = g(n-1)(a) = 0, and either f(n) (a) #0 or g(n) (a) #0 (or both); then f(x) lim: x→a g(x) ∞ f(n) (a) g(n) (a) if g(n)(a) = 0, otherwise. (Suggestion: Use Taylor's formula with Lagrange's form of the remainder, for both f(a+Ax) and g(a + Ax).)
Transcribed Image Text:== 3.14. Prove l'Hôpital's rule in the following form. Suppose f(a) = f'(a) = .. f(n-1)(a) = 0, g(a) = g'(a) = ... = g(n-1)(a) = 0, and either f(n) (a) #0 or g(n) (a) #0 (or both); then f(x) lim: x→a g(x) ∞ f(n) (a) g(n) (a) if g(n)(a) = 0, otherwise. (Suggestion: Use Taylor's formula with Lagrange's form of the remainder, for both f(a+Ax) and g(a + Ax).)
Expert Solution
steps

Step by step

Solved in 2 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