Calculus: Early Transcendentals
4th Edition
ISBN: 9781319050740
Author: Jon Rogawski, Colin Adams, Robert Franzosa
Publisher: W. H. Freeman
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Chapter 14.2, Problem 2PQ
To determine
Toevaluate:
the value of
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Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering-
Al musayab
Subject :Numerical Analysis
Stage:Third
Time: 2 hour
Automobile Department
Date:26-3-2023
nd
1st month exam/2"
semester (2022-2023)
Note: Answer all questions, all questions have same degree.
Q1: Use Newton's method to find solutions to the system with two
step Take (X,Yo)=(8,10).
{
x35x2 + 2xy + 13 = 0
x3 + x²-14x-y-19=0
Q2/:Solve the system by Gauss-Seidel iterative method.(Perform only
three iterations).
8x-3y+2z-20
4x+11y-z-33
6x+3y+12z-35
03/:Curve fit the data using a power function
X
2
4
8
5
6
0.7500
0.1875
0.1200
0.0833
0.0469
University of Babylon
Faculty of Engineering-AlMusyab
Automobile Eng. Dep.
Year: 2022-2023,
2nd Course, 1 Attempt
Stage: Third
Subject: Numerical
Analysis
Date: 2023\\
Time: 3 Hour
dy
= x + yl
Q5-A: Using Euler's method, find an approximate value
of (y) corresponding to (x=0.3),given that[-
and [y=1 when x=0].(taking h=0.1).
dx
(10 M)
Q5-B Find a root of an equation[f(x)=x-x-1] using
Newton Raphson method to an accuracy of &=0.
(10 M)
Q6:Using Newton's divided differences formula, evaluate
f(8) given:
X
4
58 7 103 11
13
Y=f(x)
48
100
900
294
1210
2028
(20 M)
Lexaminer:
Examiner:
Good luck
W
Head of Department:
Explain the conditions under which the Radius of Convergence of the Power Series is a "finite positive real number" r>0
Chapter 14 Solutions
Calculus: Early Transcendentals
Ch. 14.1 - Prob. 1PQCh. 14.1 - Prob. 2PQCh. 14.1 - Prob. 3PQCh. 14.1 - Prob. 4PQCh. 14.1 - Prob. 5PQCh. 14.1 - Prob. 1ECh. 14.1 - Prob. 2ECh. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5E
Ch. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - Prob. 10ECh. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.1 - Prob. 16ECh. 14.1 - Prob. 17ECh. 14.1 - Prob. 18ECh. 14.1 - Prob. 19ECh. 14.1 - Prob. 20ECh. 14.1 - Prob. 21ECh. 14.1 - Prob. 22ECh. 14.1 - Prob. 23ECh. 14.1 - Prob. 24ECh. 14.1 - Prob. 25ECh. 14.1 - Prob. 26ECh. 14.1 - Prob. 27ECh. 14.1 - Prob. 28ECh. 14.1 - Prob. 29ECh. 14.1 - Prob. 30ECh. 14.1 - Prob. 31ECh. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.1 - Prob. 34ECh. 14.1 - Prob. 35ECh. 14.1 - Prob. 36ECh. 14.1 - Prob. 37ECh. 14.1 - Prob. 38ECh. 14.1 - Prob. 39ECh. 14.1 - Prob. 40ECh. 14.1 - Prob. 41ECh. 14.1 - Prob. 42ECh. 14.1 - Prob. 43ECh. 14.1 - Prob. 44ECh. 14.1 - Prob. 45ECh. 14.1 - Prob. 46ECh. 14.1 - Prob. 47ECh. 14.1 - Prob. 48ECh. 14.1 - Prob. 49ECh. 14.1 - Prob. 50ECh. 14.1 - Prob. 51ECh. 14.1 - Prob. 52ECh. 14.1 - Prob. 53ECh. 14.1 - Prob. 54ECh. 14.1 - Prob. 55ECh. 14.1 - Prob. 56ECh. 14.1 - Prob. 57ECh. 14.1 - Prob. 58ECh. 14.1 - Prob. 59ECh. 14.1 - Prob. 60ECh. 14.1 - Prob. 61ECh. 14.2 - Prob. 1PQCh. 14.2 - Prob. 2PQCh. 14.2 - Prob. 3PQCh. 14.2 - Prob. 4PQCh. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Prob. 12ECh. 14.2 - Prob. 13ECh. 14.2 - Prob. 14ECh. 14.2 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - Prob. 21ECh. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - Prob. 27ECh. 14.2 - Prob. 28ECh. 14.2 - Prob. 29ECh. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - Prob. 33ECh. 14.2 - Prob. 34ECh. 14.2 - Prob. 35ECh. 14.2 - Prob. 36ECh. 14.2 - Prob. 37ECh. 14.2 - Prob. 38ECh. 14.2 - Prob. 39ECh. 14.2 - Prob. 40ECh. 14.2 - Prob. 41ECh. 14.2 - Prob. 42ECh. 14.2 - Prob. 43ECh. 14.2 - Prob. 44ECh. 14.2 - Prob. 45ECh. 14.2 - Prob. 46ECh. 14.2 - Prob. 47ECh. 14.2 - Prob. 48ECh. 14.2 - Prob. 49ECh. 14.2 - Prob. 50ECh. 14.2 - Prob. 51ECh. 14.3 - Prob. 1PQCh. 14.3 - Prob. 2PQCh. 14.3 - Prob. 3PQCh. 14.3 - Prob. 4PQCh. 14.3 - Prob. 5PQCh. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - Prob. 3ECh. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Prob. 14ECh. 14.3 - Prob. 15ECh. 14.3 - Prob. 16ECh. 14.3 - Prob. 17ECh. 14.3 - Prob. 18ECh. 14.3 - Prob. 19ECh. 14.3 - Prob. 20ECh. 14.3 - Prob. 21ECh. 14.3 - Prob. 22ECh. 14.3 - Prob. 23ECh. 14.3 - Prob. 24ECh. 14.3 - Prob. 25ECh. 14.3 - Prob. 26ECh. 14.3 - Prob. 27ECh. 14.3 - Prob. 28ECh. 14.3 - Prob. 29ECh. 14.3 - Prob. 30ECh. 14.3 - Prob. 31ECh. 14.3 - Prob. 32ECh. 14.3 - Prob. 33ECh. 14.3 - Prob. 34ECh. 14.3 - Prob. 35ECh. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - Prob. 38ECh. 14.3 - Prob. 39ECh. 14.3 - Prob. 40ECh. 14.3 - Prob. 41ECh. 14.3 - Prob. 42ECh. 14.3 - Prob. 43ECh. 14.3 - Prob. 44ECh. 14.3 - Prob. 45ECh. 14.3 - Prob. 46ECh. 14.3 - Prob. 47ECh. 14.3 - Prob. 48ECh. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.3 - Prob. 51ECh. 14.3 - Prob. 52ECh. 14.3 - Prob. 53ECh. 14.3 - Prob. 54ECh. 14.3 - Prob. 55ECh. 14.3 - Prob. 56ECh. 14.3 - Prob. 57ECh. 14.3 - Prob. 58ECh. 14.3 - Prob. 59ECh. 14.3 - Prob. 60ECh. 14.3 - Prob. 61ECh. 14.3 - Prob. 62ECh. 14.3 - Prob. 63ECh. 14.3 - Prob. 64ECh. 14.3 - Prob. 65ECh. 14.3 - Prob. 66ECh. 14.3 - Prob. 67ECh. 14.3 - Prob. 68ECh. 14.3 - Prob. 69ECh. 14.3 - Prob. 70ECh. 14.3 - Prob. 71ECh. 14.3 - Prob. 72ECh. 14.3 - Prob. 73ECh. 14.3 - Prob. 74ECh. 14.3 - Prob. 75ECh. 14.3 - Prob. 76ECh. 14.3 - Prob. 77ECh. 14.3 - Prob. 78ECh. 14.3 - Prob. 79ECh. 14.3 - Prob. 80ECh. 14.4 - Prob. 1PQCh. 14.4 - Prob. 2PQCh. 14.4 - Prob. 3PQCh. 14.4 - Prob. 4PQCh. 14.4 - Prob. 5PQCh. 14.4 - Prob. 6PQCh. 14.4 - Prob. 1ECh. 14.4 - Prob. 2ECh. 14.4 - Prob. 3ECh. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - Prob. 6ECh. 14.4 - Prob. 7ECh. 14.4 - Prob. 8ECh. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Prob. 24ECh. 14.4 - Prob. 25ECh. 14.4 - Prob. 26ECh. 14.4 - Prob. 27ECh. 14.4 - Prob. 28ECh. 14.4 - Prob. 29ECh. 14.4 - Prob. 30ECh. 14.4 - Prob. 31ECh. 14.4 - Prob. 32ECh. 14.4 - Prob. 33ECh. 14.4 - Prob. 34ECh. 14.4 - Prob. 35ECh. 14.4 - Prob. 36ECh. 14.4 - Prob. 37ECh. 14.4 - Prob. 38ECh. 14.4 - Prob. 39ECh. 14.4 - Prob. 40ECh. 14.4 - Prob. 41ECh. 14.4 - Prob. 42ECh. 14.4 - Prob. 43ECh. 14.4 - Prob. 44ECh. 14.4 - Prob. 45ECh. 14.4 - Prob. 46ECh. 14.4 - Prob. 47ECh. 14.5 - Prob. 1PQCh. 14.5 - Prob. 2PQCh. 14.5 - Prob. 3PQCh. 14.5 - Prob. 4PQCh. 14.5 - Prob. 5PQCh. 14.5 - Prob. 1ECh. 14.5 - Prob. 2ECh. 14.5 - Prob. 3ECh. 14.5 - Prob. 4ECh. 14.5 - Prob. 5ECh. 14.5 - Prob. 6ECh. 14.5 - Prob. 7ECh. 14.5 - Prob. 8ECh. 14.5 - Prob. 9ECh. 14.5 - Prob. 10ECh. 14.5 - Prob. 11ECh. 14.5 - Prob. 12ECh. 14.5 - Prob. 13ECh. 14.5 - Prob. 14ECh. 14.5 - Prob. 15ECh. 14.5 - Prob. 16ECh. 14.5 - Prob. 17ECh. 14.5 - Prob. 18ECh. 14.5 - Prob. 19ECh. 14.5 - Prob. 20ECh. 14.5 - Prob. 21ECh. 14.5 - Prob. 22ECh. 14.5 - Prob. 23ECh. 14.5 - Prob. 24ECh. 14.5 - Prob. 25ECh. 14.5 - Prob. 26ECh. 14.5 - Prob. 27ECh. 14.5 - Prob. 28ECh. 14.5 - Prob. 29ECh. 14.5 - Prob. 30ECh. 14.5 - Prob. 31ECh. 14.5 - Prob. 32ECh. 14.5 - Prob. 33ECh. 14.5 - Prob. 34ECh. 14.5 - Prob. 35ECh. 14.5 - Prob. 36ECh. 14.5 - Prob. 37ECh. 14.5 - Prob. 38ECh. 14.5 - Prob. 39ECh. 14.5 - Prob. 40ECh. 14.5 - Prob. 41ECh. 14.5 - Prob. 42ECh. 14.5 - Prob. 43ECh. 14.5 - Prob. 44ECh. 14.5 - Prob. 45ECh. 14.5 - Prob. 46ECh. 14.5 - Prob. 47ECh. 14.5 - Prob. 48ECh. 14.5 - Prob. 49ECh. 14.5 - Prob. 50ECh. 14.5 - Prob. 51ECh. 14.5 - Prob. 52ECh. 14.5 - Prob. 53ECh. 14.5 - Prob. 54ECh. 14.5 - Prob. 55ECh. 14.5 - Prob. 56ECh. 14.5 - Prob. 57ECh. 14.5 - Prob. 58ECh. 14.5 - Prob. 59ECh. 14.5 - Prob. 60ECh. 14.5 - Prob. 61ECh. 14.5 - Prob. 62ECh. 14.5 - Prob. 63ECh. 14.5 - Prob. 64ECh. 14.5 - Prob. 65ECh. 14.5 - Prob. 66ECh. 14.5 - Prob. 67ECh. 14.5 - Prob. 68ECh. 14.5 - Prob. 69ECh. 14.5 - Prob. 70ECh. 14.5 - Prob. 71ECh. 14.5 - Prob. 72ECh. 14.5 - Prob. 73ECh. 14.5 - Prob. 74ECh. 14.5 - Prob. 75ECh. 14.5 - Prob. 76ECh. 14.5 - Prob. 77ECh. 14.6 - Prob. 1PQCh. 14.6 - Prob. 2PQCh. 14.6 - Prob. 3PQCh. 14.6 - Prob. 4PQCh. 14.6 - Prob. 5PQCh. 14.6 - Prob. 6PQCh. 14.6 - Prob. 1ECh. 14.6 - Prob. 2ECh. 14.6 - Prob. 3ECh. 14.6 - Prob. 4ECh. 14.6 - Prob. 5ECh. 14.6 - Prob. 6ECh. 14.6 - Prob. 7ECh. 14.6 - Prob. 8ECh. 14.6 - Prob. 9ECh. 14.6 - Prob. 10ECh. 14.6 - Prob. 11ECh. 14.6 - Prob. 12ECh. 14.6 - Prob. 13ECh. 14.6 - Prob. 14ECh. 14.6 - Prob. 15ECh. 14.6 - Prob. 16ECh. 14.6 - Prob. 17ECh. 14.6 - Prob. 18ECh. 14.6 - Prob. 19ECh. 14.6 - Prob. 20ECh. 14.6 - Prob. 21ECh. 14.6 - Prob. 22ECh. 14.6 - Prob. 23ECh. 14.6 - Prob. 24ECh. 14.6 - Prob. 25ECh. 14.6 - Prob. 26ECh. 14.6 - Prob. 27ECh. 14.6 - Prob. 28ECh. 14.6 - Prob. 29ECh. 14.6 - Prob. 30ECh. 14.6 - Prob. 31ECh. 14.6 - Prob. 32ECh. 14.6 - Prob. 33ECh. 14.6 - Prob. 34ECh. 14.6 - Prob. 35ECh. 14.6 - Prob. 36ECh. 14.6 - Prob. 37ECh. 14.6 - Prob. 38ECh. 14.6 - Prob. 39ECh. 14.6 - Prob. 40ECh. 14.6 - Prob. 41ECh. 14.6 - Prob. 42ECh. 14.6 - Prob. 43ECh. 14.6 - Prob. 44ECh. 14.6 - Prob. 45ECh. 14.6 - Prob. 46ECh. 14.6 - Prob. 47ECh. 14.6 - Prob. 48ECh. 14.6 - Prob. 49ECh. 14.6 - Prob. 50ECh. 14.6 - Prob. 51ECh. 14.6 - Prob. 52ECh. 14.6 - Prob. 53ECh. 14.6 - Prob. 54ECh. 14.6 - Prob. 55ECh. 14.7 - Prob. 1PQCh. 14.7 - Prob. 2PQCh. 14.7 - Prob. 3PQCh. 14.7 - Prob. 1ECh. 14.7 - Prob. 2ECh. 14.7 - Prob. 3ECh. 14.7 - Prob. 4ECh. 14.7 - Prob. 5ECh. 14.7 - Prob. 6ECh. 14.7 - Prob. 7ECh. 14.7 - Prob. 8ECh. 14.7 - Prob. 9ECh. 14.7 - Prob. 10ECh. 14.7 - Prob. 11ECh. 14.7 - Prob. 12ECh. 14.7 - Prob. 13ECh. 14.7 - Prob. 14ECh. 14.7 - Prob. 15ECh. 14.7 - Prob. 16ECh. 14.7 - Prob. 17ECh. 14.7 - Prob. 18ECh. 14.7 - Prob. 19ECh. 14.7 - Prob. 20ECh. 14.7 - Prob. 21ECh. 14.7 - Prob. 22ECh. 14.7 - Prob. 23ECh. 14.7 - Prob. 24ECh. 14.7 - Prob. 25ECh. 14.7 - Prob. 26ECh. 14.7 - Prob. 27ECh. 14.7 - Prob. 28ECh. 14.7 - Prob. 29ECh. 14.7 - Prob. 30ECh. 14.7 - Prob. 31ECh. 14.7 - Prob. 32ECh. 14.7 - Prob. 33ECh. 14.7 - Prob. 34ECh. 14.7 - Prob. 35ECh. 14.7 - Prob. 36ECh. 14.7 - Prob. 37ECh. 14.7 - Prob. 38ECh. 14.7 - Prob. 39ECh. 14.7 - Prob. 40ECh. 14.7 - Prob. 41ECh. 14.7 - Prob. 42ECh. 14.7 - Prob. 43ECh. 14.7 - Prob. 44ECh. 14.7 - Prob. 45ECh. 14.7 - Prob. 46ECh. 14.7 - Prob. 47ECh. 14.7 - Prob. 48ECh. 14.7 - Prob. 49ECh. 14.7 - Prob. 50ECh. 14.7 - Prob. 51ECh. 14.7 - Prob. 52ECh. 14.7 - Prob. 53ECh. 14.7 - Prob. 54ECh. 14.7 - Prob. 55ECh. 14.7 - Prob. 56ECh. 14.7 - Prob. 57ECh. 14.7 - Prob. 58ECh. 14.7 - Prob. 59ECh. 14.7 - Prob. 60ECh. 14.7 - Prob. 61ECh. 14.7 - Prob. 62ECh. 14.7 - Prob. 63ECh. 14.7 - Prob. 64ECh. 14.8 - Prob. 1PQCh. 14.8 - Prob. 2PQCh. 14.8 - Prob. 3PQCh. 14.8 - Prob. 1ECh. 14.8 - Prob. 2ECh. 14.8 - Prob. 3ECh. 14.8 - Prob. 4ECh. 14.8 - Prob. 5ECh. 14.8 - Prob. 6ECh. 14.8 - Prob. 7ECh. 14.8 - Prob. 8ECh. 14.8 - Prob. 9ECh. 14.8 - Prob. 10ECh. 14.8 - Prob. 11ECh. 14.8 - Prob. 12ECh. 14.8 - Prob. 13ECh. 14.8 - Prob. 14ECh. 14.8 - Prob. 15ECh. 14.8 - Prob. 16ECh. 14.8 - Prob. 17ECh. 14.8 - Prob. 18ECh. 14.8 - Prob. 19ECh. 14.8 - Prob. 20ECh. 14.8 - Prob. 21ECh. 14.8 - Prob. 22ECh. 14.8 - Prob. 23ECh. 14.8 - Prob. 24ECh. 14.8 - Prob. 25ECh. 14.8 - Prob. 26ECh. 14.8 - Prob. 27ECh. 14.8 - Prob. 28ECh. 14.8 - Prob. 29ECh. 14.8 - Prob. 30ECh. 14.8 - Prob. 31ECh. 14.8 - Prob. 32ECh. 14.8 - Prob. 33ECh. 14.8 - Prob. 34ECh. 14.8 - Prob. 35ECh. 14.8 - Prob. 36ECh. 14.8 - Prob. 37ECh. 14.8 - Prob. 38ECh. 14.8 - Prob. 39ECh. 14.8 - Prob. 40ECh. 14.8 - Prob. 41ECh. 14.8 - Prob. 42ECh. 14.8 - Prob. 43ECh. 14.8 - Prob. 44ECh. 14.8 - Prob. 45ECh. 14.8 - Prob. 46ECh. 14.8 - Prob. 47ECh. 14.8 - Prob. 48ECh. 14.8 - Prob. 49ECh. 14.8 - Prob. 50ECh. 14.8 - Prob. 51ECh. 14.8 - Prob. 52ECh. 14.8 - Prob. 53ECh. 14.8 - Prob. 54ECh. 14.8 - Prob. 55ECh. 14.8 - Prob. 56ECh. 14 - Prob. 1CRECh. 14 - Prob. 2CRECh. 14 - Prob. 3CRECh. 14 - Prob. 4CRECh. 14 - Prob. 5CRECh. 14 - Prob. 6CRECh. 14 - Prob. 7CRECh. 14 - Prob. 8CRECh. 14 - Prob. 9CRECh. 14 - Prob. 10CRECh. 14 - Prob. 11CRECh. 14 - Prob. 12CRECh. 14 - Prob. 13CRECh. 14 - Prob. 14CRECh. 14 - Prob. 15CRECh. 14 - Prob. 16CRECh. 14 - Prob. 17CRECh. 14 - Prob. 18CRECh. 14 - Prob. 19CRECh. 14 - Prob. 20CRECh. 14 - Prob. 21CRECh. 14 - Prob. 22CRECh. 14 - Prob. 23CRECh. 14 - Prob. 24CRECh. 14 - Prob. 25CRECh. 14 - Prob. 26CRECh. 14 - Prob. 27CRECh. 14 - Prob. 28CRECh. 14 - Prob. 29CRECh. 14 - Prob. 30CRECh. 14 - Prob. 31CRECh. 14 - Prob. 32CRECh. 14 - Prob. 33CRECh. 14 - Prob. 34CRECh. 14 - Prob. 35CRECh. 14 - Prob. 36CRECh. 14 - Prob. 37CRECh. 14 - Prob. 38CRECh. 14 - Prob. 39CRECh. 14 - Prob. 40CRECh. 14 - Prob. 41CRECh. 14 - Prob. 42CRECh. 14 - Prob. 43CRECh. 14 - Prob. 44CRECh. 14 - Prob. 45CRECh. 14 - Prob. 46CRECh. 14 - Prob. 47CRECh. 14 - Prob. 48CRECh. 14 - Prob. 49CRECh. 14 - Prob. 50CRECh. 14 - Prob. 51CRECh. 14 - Prob. 52CRECh. 14 - Prob. 53CRECh. 14 - Prob. 54CRECh. 14 - Prob. 55CRECh. 14 - Prob. 56CRECh. 14 - Prob. 57CRECh. 14 - Prob. 58CRECh. 14 - Prob. 59CRECh. 14 - Prob. 60CRECh. 14 - Prob. 61CRECh. 14 - Prob. 62CRECh. 14 - Prob. 63CRE
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- This means that when the Radius of Convergence of the Power Series is a "finite positive real number" r>0, then every point x of the Power Series on (-r, r) will absolutely converge (x ∈ (-r, r)). Moreover, every point x on the Power Series (-∞, -r)U(r, +∞) will diverge (|x| >r). Please explain it.arrow_forwardExplain the conditions under which Radious of Convergence of Power Series is infinite. Explain what will happen?arrow_forwardExplain the conditions under Radius of Convergence which of Power Series is 0arrow_forward
- Explain the key points and reasons for 12.8.2 (1) and 12.8.2 (2)arrow_forwardQ1: A slider in a machine moves along a fixed straight rod. Its distance x cm along the rod is given below for various values of the time. Find the velocity and acceleration of the slider when t = 0.3 seconds. t(seconds) x(cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 30.13 31.62 32.87 33.64 33.95 33.81 33.24 Q2: Using the Runge-Kutta method of fourth order, solve for y atr = 1.2, From dy_2xy +et = dx x²+xc* Take h=0.2. given x = 1, y = 0 Q3:Approximate the solution of the following equation using finite difference method. ly -(1-y= y = x), y(1) = 2 and y(3) = −1 On the interval (1≤x≤3).(taking h=0.5).arrow_forwardConsider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?arrow_forward
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