Math 152 Week 13 Workshop Problems Write up your solutions to each of these problems on a seperate sheet of paper. sin(x) 1. Let f(x)= Also, define f(0) = 1. I 4/8/24 (a) Using known Maclaurin series and power series operations, find the Maclaurin series for f(x). (b) The sine integral is defined by Si(z) = f(t) dt. Find the Maclaurin series for Si(z) (c) Use the first two non-zero terms of your series from part b) to approximate Si(0.5). 2. Using power series, evaluate lim x ln(1 + 2x³) 2-0 1- cos(3x2) 3. Consider the series 1 1 A). 3.3 32.5 + 33.7 (a) Find a formula for a general term of this series. (b) Using the Alternating Series Error Estimation Theorem, determine the error in using the first 3 terms of the series to approximate the sum of the series. (c) Find the exact value of the sum of the series.
Math 152 Week 13 Workshop Problems Write up your solutions to each of these problems on a seperate sheet of paper. sin(x) 1. Let f(x)= Also, define f(0) = 1. I 4/8/24 (a) Using known Maclaurin series and power series operations, find the Maclaurin series for f(x). (b) The sine integral is defined by Si(z) = f(t) dt. Find the Maclaurin series for Si(z) (c) Use the first two non-zero terms of your series from part b) to approximate Si(0.5). 2. Using power series, evaluate lim x ln(1 + 2x³) 2-0 1- cos(3x2) 3. Consider the series 1 1 A). 3.3 32.5 + 33.7 (a) Find a formula for a general term of this series. (b) Using the Alternating Series Error Estimation Theorem, determine the error in using the first 3 terms of the series to approximate the sum of the series. (c) Find the exact value of the sum of the series.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Math 152
Week 13 Workshop Problems
Write up your solutions to each of these problems on a seperate sheet of paper.
sin(x)
1. Let f(x)=
Also, define f(0) = 1.
I
4/8/24
(a) Using known Maclaurin series and power series operations, find the Maclaurin series for f(x).
(b) The sine integral is defined by Si(z) = f(t) dt. Find the Maclaurin series for Si(z)
(c) Use the first two non-zero terms of your series from part b) to approximate Si(0.5).
2. Using power series, evaluate lim
x ln(1 + 2x³)
2-0 1- cos(3x2)
3. Consider the series
1
1
A).
3.3 32.5
+
33.7
(a) Find a formula for a general term of this series.
(b) Using the Alternating Series Error Estimation Theorem, determine the error in using the first 3
terms of the series to approximate the sum of the series.
(c) Find the exact value of the sum of the series.
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