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Math 152 Week 12 Workshop Problems 4/1/24 Write up your solutions to each of these problems on a seperate sheet of paper. 1. For each of the given functions, find the Taylor polynomial with the degree and center indicated. (a) Find T3(2), the third degree Taylor polynomial, for f(x) = tan(2x) centered at c= πT (b) Find T2(x), the second degree Taylor polynomial, for f(x) = 2+3x centered at c = 2. -

Math 152 Week 12 Workshop Problems 4/1/24 Write up your solutions to each of these problems on a seperate sheet of paper. 1. For each of the given functions, find the Taylor polynomial with the degree and center indicated. (a) Find T3(2), the third degree Taylor polynomial, for f(x) = tan(2x) centered at c= πT (b) Find T2(x), the second degree Taylor polynomial, for f(x) = 2+3x centered at c = 2. -

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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Question 1 and 3 please!
Math 152 Week 12 Workshop Problems 4/1/24 Write up your solutions to each of these problems on a seperate sheet of paper. 1. For each of the given functions, find the Taylor polynomial with the degree and center indicated. (a) Find T3(2), the third degree Taylor polynomial, for f(x) = tan(2x) centered at c = ה (b) Find T2(x), the second degree Taylor polynomial, for f(x)=√2+3x centered at c = 2. 2. (a) Find T4(2), the 4th order Taylor polynomial centered at x=1, for In(r). (b) Use T4(x) to approximate the value of In(1.5). Then use the Taylor Remainder Estimation Theorem to estimate the error in approximating In(1.5) with this Taylor polynomial. (c) Would the expected error increase or decrease if we use Ts (2) to estimate In(1.5)? Would the expected error increase or decrease if we use T4(r) to estimate In(1.9)? Explain each of your answers in a sentence or two. 3. For each of the given functions, find the Taylor series for the function centered at the indicated value. (a) f(z) = e/2, c = 2 T (b) f(x) = cos(2), c =
Transcribed Image Text:Math 152 Week 12 Workshop Problems 4/1/24 Write up your solutions to each of these problems on a seperate sheet of paper. 1. For each of the given functions, find the Taylor polynomial with the degree and center indicated. (a) Find T3(2), the third degree Taylor polynomial, for f(x) = tan(2x) centered at c = ה (b) Find T2(x), the second degree Taylor polynomial, for f(x)=√2+3x centered at c = 2. 2. (a) Find T4(2), the 4th order Taylor polynomial centered at x=1, for In(r). (b) Use T4(x) to approximate the value of In(1.5). Then use the Taylor Remainder Estimation Theorem to estimate the error in approximating In(1.5) with this Taylor polynomial. (c) Would the expected error increase or decrease if we use Ts (2) to estimate In(1.5)? Would the expected error increase or decrease if we use T4(r) to estimate In(1.9)? Explain each of your answers in a sentence or two. 3. For each of the given functions, find the Taylor series for the function centered at the indicated value. (a) f(z) = e/2, c = 2 T (b) f(x) = cos(2), c =
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