Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
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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Question 8 pls
![8.1 EXERCISES
In Problems 1-8, determine the first three nonzero terms in
the Taylor polynomial approximations for the given initial
value problem.
1. y' = x² + y²;
2. y' = y²; y (0) = 2
3. y'= siny+ e*;
4. y'= sin(x+y);
5. x" + tx = 0;
2
y(0) = 1
6. y" + y = 0;
7. y" (0) + y(0)³ = sin0;
y(0) = 0,
I 8. y" + siny = 0;
3
x(0) = 1,
y (0) = 0,
80
y(0) = 0
y(0) = 0
y'(0) = 0
y' (0) = 0
9. (a) Construct the Taylor polynomial p3(x) of degree 3
for the function f(x) = ln x around x = 1.
(b) Using the error formula (6), show that
y (0) = 1,
(0.5)4
In (1.5) - P3 (1.5) |
= 0.015625.
4
(c) Compare the estimate in part (b) with the actual
error by calculating In (1.5) - P3 (1.5).
(d) Sketch the graphs of ln x and p(x) (on the same
$
4
x' (0) = 0
y' (0) = 1
888
%
5
^
6
F6
7
*
(d) S
sa
8
11. Argue
equati-
(a, b)
then th
12. Argue
equatic
val (a-
orders,
13. Duffing
with pe
y"
Let k =
nonzerc
to the sc
14. Soft v
tion giv
changes
force ky
(r = 0)
restoring](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe38cc688-b545-4be2-9b11-6e87392e9973%2Fa5ee26b8-b7b7-4c3e-87d3-6b4b6d912e6d%2Fjxhxa49_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8.1 EXERCISES
In Problems 1-8, determine the first three nonzero terms in
the Taylor polynomial approximations for the given initial
value problem.
1. y' = x² + y²;
2. y' = y²; y (0) = 2
3. y'= siny+ e*;
4. y'= sin(x+y);
5. x" + tx = 0;
2
y(0) = 1
6. y" + y = 0;
7. y" (0) + y(0)³ = sin0;
y(0) = 0,
I 8. y" + siny = 0;
3
x(0) = 1,
y (0) = 0,
80
y(0) = 0
y(0) = 0
y'(0) = 0
y' (0) = 0
9. (a) Construct the Taylor polynomial p3(x) of degree 3
for the function f(x) = ln x around x = 1.
(b) Using the error formula (6), show that
y (0) = 1,
(0.5)4
In (1.5) - P3 (1.5) |
= 0.015625.
4
(c) Compare the estimate in part (b) with the actual
error by calculating In (1.5) - P3 (1.5).
(d) Sketch the graphs of ln x and p(x) (on the same
$
4
x' (0) = 0
y' (0) = 1
888
%
5
^
6
F6
7
*
(d) S
sa
8
11. Argue
equati-
(a, b)
then th
12. Argue
equatic
val (a-
orders,
13. Duffing
with pe
y"
Let k =
nonzerc
to the sc
14. Soft v
tion giv
changes
force ky
(r = 0)
restoring
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