ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<
4th Edition
ISBN: 9781319411657
Author: Rogawski
Publisher: MAC HIGHER
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Chapter 14.5, Problem 52E
To determine
To find function
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Evaluate the following integrals, showing all your working
Consider the function f(x) = 2x³-4x2-x+1.
(a) Without doing a sketch, show that the cubic equation has at least one solution on the interval
[0,1]. Use a theorem discussed in lectures, or see Section 1.8 of Calculus (7th ed) by Stewart.
Ensure that the conditions of the theorem are satisfied (include this in your solution)
(b) Now, by sketching the cubic (by hand or by computer), you should see that there is, in fact,
exactly one zero in the interval [0,1]. Use Newton's method to find this zero accurate to 3
decimal places. You should include a sketch of the cubic, Newton's iteration formula, and
the list of iterates. [Use a computer if possible, e.g., a spreadsheet or MatLab.]
Evaluate the following integrals, showing all your working
Chapter 14 Solutions
ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<
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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- Consider the equation, f(x) = x*. (a) Using the trapezoidal method with 3 columns, estimate the value of the integral f² f(x)dx. (b) Using the trapezoidal method with 10 columns, estimate the value of the integral f² f(x)dx. You many need software to help you do this (e.g. MATLAB, Excel, Google sheets). (c) Use software to accurately calculate the integral (e.g. Wolfram alpha, Matlab). Using this answer, comment on the answers you found in parts a) and b).arrow_forwardUsing the first-principles definition of differentiation, find the derivative of f(x) = = 2x²arrow_forwardEvaluate the following integrals, showing all your workingarrow_forward
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