Question 18: Using c = 0 as the centre, show that for all I ER, ²n+1 (2n + 1)! sin(x)=(-1)" n=0 (Hint: Find the Taylor polynomial of degree n, P(x), and the remainder term R₁(1), and show that as n →∞, with some reasonable bound on f(d), we have R₂(1)→0.) OC
Question 18: Using c = 0 as the centre, show that for all I ER, ²n+1 (2n + 1)! sin(x)=(-1)" n=0 (Hint: Find the Taylor polynomial of degree n, P(x), and the remainder term R₁(1), and show that as n →∞, with some reasonable bound on f(d), we have R₂(1)→0.) OC
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
Related questions
Question
![Question 18: Using c = 0 as the centre, show that for all & ER,
2n+1
(2n + 1)!
sin(x)=(-1)",
n=0
(Hint: Find the Taylor polynomial of degree n, P(x), and the remainder term R₁(x),
and show that as n → ∞, with some reasonable bound on f(d), we have R₁(x) →0.)
OC
€](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6ab55cb-bf08-43d5-b773-a7fb5882b2b9%2F903045cb-1b57-4288-93e5-352365668285%2Fhxxi9cu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 18: Using c = 0 as the centre, show that for all & ER,
2n+1
(2n + 1)!
sin(x)=(-1)",
n=0
(Hint: Find the Taylor polynomial of degree n, P(x), and the remainder term R₁(x),
and show that as n → ∞, with some reasonable bound on f(d), we have R₁(x) →0.)
OC
€
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