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#1: By Taylor's theorem, we can find a Taylor polynomial P3(1) of degree 3 for the function g(t) = cos(2t) sin(31) near/= 0 such that g(1) = P3(1) + R3(0, 1) in some interval where R3(0, 1) is the remainder term. Writing P3(1) as P3(1)= a+at+az² + azt³, calculate the coefficient a3.

#1: By Taylor's theorem, we can find a Taylor polynomial P3(1) of degree 3 for the function g(t) = cos(2t) sin(31) near/= 0 such that g(1) = P3(1) + R3(0, 1) in some interval where R3(0, 1) is the remainder term. Writing P3(1) as P3(1)= a+at+az² + azt³, calculate the coefficient a3.

Algebra & Trigonometry with Analytic Geometry
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
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#1: By Taylor's theorem, we can find a Taylor polynomial P3(1) of degree 3 for the function g(t) = cos(2t) sin(31) near/= 0 such that g(1) = P3(1) + R3(0, 1) in some interval where R3(0, 1) is the remainder term. Writing P3(1) as P3(1)= a+at+az² + azt³, calculate the coefficient a3.
Transcribed Image Text:#1: By Taylor's theorem, we can find a Taylor polynomial P3(1) of degree 3 for the function g(t) = cos(2t) sin(31) near/= 0 such that g(1) = P3(1) + R3(0, 1) in some interval where R3(0, 1) is the remainder term. Writing P3(1) as P3(1)= a+at+az² + azt³, calculate the coefficient a3.
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