Problem #1: By Taylor's theorem, we can find a Taylor polynomial P3(+) of degree 3 for the functiong(t)cos(5) sin(47) near =0 such thatg(1) P3(1)+R3(0, 1)in some interval where R3(0, 1) is the remainder term. Writing P3(1) asP3(1)= a+at+a21² + azt³,calculate the coefficient a3.

Given: To Find: To calculate the coefficient .

Problem #1: By Taylor's theorem, we can find a Taylor polynomial P3(f) of degree 3 for the function g(f) cos(5) sin(4) 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)= ao+at+ azt²+az1³, calculate the coefficient a3.

Problem #1: By Taylor's theorem, we can find a Taylor polynomial P3(f) of degree 3 for the function g(f) cos(5) sin(4) 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)= ao+at+ azt²+az1³, calculate the coefficient a3.

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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Question

Problem #1: By Taylor's theorem, we can find a Taylor polynomial P3(+) of degree 3 for the function
g(t)
cos(5) sin(47) 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+a21² + azt³,
calculate the coefficient a3.

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Step 1: Define the problem.

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Step 2: Find the derivatives of the function.

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Step 3: Define the Taylor polynomial of degree 3 for the given function.

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Step 4: Solve for the unknown coefficient.

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