==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 org(n) (a) #0 (or both); thenf(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, forboth f(a+Ax) and g(a + Ax).)

Given :f(a)=f'(a)=....=f(n-1)(a)=0 , g(a)=g'(a)=...=g(n-1)(a)=0 We have to prove :…

== 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).)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 5T

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