Loose-leaf Version For Calculus: Early Transcendentals
4th Edition
ISBN: 9781319055912
Author: Jon Rogawski, Colin Adams, Robert Franzosa
Publisher: W. H. Freeman
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Chapter 1.1, Problem 63E
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(x)=2x-x2
2
a=2, b = 1/2, C=0
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F(x)=ax 2 + bx + c
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Za
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JANUARY 17, 2025
WORKSHEET 1
Solve the following four problems on a separate sheet. Fully justify your answers to
MATH 122
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earn full credit.
1. Let f(x) = 2x-
1x2
2
(a) Rewrite this quadratic function in standard form: f(x) = ax² + bx + c
and indicate the values of the coefficients: a, b and c.
(b) Find the vertex V, focus F, focal width, directrix D, and the axis of
symmetry for the graph of y = f(x).
(c) Plot a graph of y = f(x) and indicate all quantities found in part (b)
on your graph.
(d) Specify the domain and range of the function f.
OUR
2. Let g(x) = f(x) u(x) where f is the quadratic function from problem 1
and u is the unit step function:
u(x) = { 0
1 if x ≥0
0 if x<0
y = u(x)
0
(a) Write a piecewise formula for the function g.
(b) Sketch a graph of y = g(x).
(c) Indicate the domain and range of the function g.
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where u is the unit step function defined in problem 2.
3. Let…
Question 1
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Question 3: Construct the accessibility matrix Passociated with
the following graphs, and compute P2 and identify each at the
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Chapter 1 Solutions
Loose-leaf Version For Calculus: Early Transcendentals
Ch. 1.1 - Prob. 1PQCh. 1.1 - Prob. 2PQCh. 1.1 - Prob. 3PQCh. 1.1 - Prob. 4PQCh. 1.1 - Prob. 5PQCh. 1.1 - Prob. 6PQCh. 1.1 - Prob. 7PQCh. 1.1 - Prob. 8PQCh. 1.1 - Prob. 9PQCh. 1.1 - Prob. 10PQ
Ch. 1.1 - Prob. 1ECh. 1.1 - Prob. 2ECh. 1.1 - Prob. 3ECh. 1.1 - Prob. 4ECh. 1.1 - Prob. 5ECh. 1.1 - Prob. 6ECh. 1.1 - Prob. 7ECh. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - Prob. 10ECh. 1.1 - Prob. 11ECh. 1.1 - Prob. 12ECh. 1.1 - Prob. 13ECh. 1.1 - Prob. 14ECh. 1.1 - Prob. 15ECh. 1.1 - Prob. 16ECh. 1.1 - Prob. 17ECh. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - Prob. 21ECh. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - Prob. 25ECh. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.1 - Prob. 28ECh. 1.1 - Prob. 29ECh. 1.1 - Prob. 30ECh. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - Prob. 34ECh. 1.1 - Prob. 35ECh. 1.1 - Prob. 36ECh. 1.1 - Prob. 37ECh. 1.1 - Prob. 38ECh. 1.1 - Prob. 39ECh. 1.1 - Prob. 40ECh. 1.1 - Prob. 41ECh. 1.1 - Prob. 42ECh. 1.1 - Prob. 43ECh. 1.1 - Prob. 44ECh. 1.1 - Prob. 45ECh. 1.1 - Prob. 46ECh. 1.1 - Prob. 47ECh. 1.1 - Prob. 48ECh. 1.1 - Prob. 49ECh. 1.1 - Prob. 50ECh. 1.1 - Prob. 51ECh. 1.1 - Prob. 52ECh. 1.1 - Prob. 53ECh. 1.1 - Prob. 54ECh. 1.1 - Prob. 55ECh. 1.1 - Prob. 56ECh. 1.1 - Prob. 57ECh. 1.1 - Prob. 58ECh. 1.1 - Prob. 59ECh. 1.1 - Prob. 60ECh. 1.1 - Prob. 61ECh. 1.1 - Prob. 62ECh. 1.1 - Prob. 63ECh. 1.1 - Prob. 64ECh. 1.1 - Prob. 65ECh. 1.1 - Prob. 66ECh. 1.1 - Prob. 67ECh. 1.1 - Prob. 68ECh. 1.1 - Prob. 69ECh. 1.1 - Prob. 70ECh. 1.1 - Prob. 71ECh. 1.1 - Prob. 72ECh. 1.1 - Prob. 73ECh. 1.1 - Prob. 74ECh. 1.1 - Prob. 75ECh. 1.1 - Prob. 76ECh. 1.1 - Prob. 77ECh. 1.1 - Prob. 78ECh. 1.1 - Prob. 79ECh. 1.1 - Prob. 80ECh. 1.1 - Prob. 81ECh. 1.1 - Prob. 82ECh. 1.1 - Prob. 83ECh. 1.1 - Prob. 84ECh. 1.1 - Prob. 85ECh. 1.1 - Prob. 86ECh. 1.1 - Prob. 87ECh. 1.1 - Prob. 88ECh. 1.1 - Prob. 89ECh. 1.1 - Prob. 90ECh. 1.1 - Prob. 91ECh. 1.1 - Prob. 92ECh. 1.2 - Prob. 1PQCh. 1.2 - Prob. 2PQCh. 1.2 - Prob. 3PQCh. 1.2 - Prob. 4PQCh. 1.2 - Prob. 5PQCh. 1.2 - Prob. 6PQCh. 1.2 - Prob. 7PQCh. 1.2 - Prob. 8PQCh. 1.2 - Prob. 1ECh. 1.2 - Prob. 2ECh. 1.2 - Prob. 3ECh. 1.2 - Prob. 4ECh. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - Prob. 25ECh. 1.2 - Prob. 26ECh. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - Prob. 33ECh. 1.2 - Prob. 34ECh. 1.2 - Prob. 35ECh. 1.2 - Prob. 36ECh. 1.2 - Prob. 37ECh. 1.2 - Prob. 38ECh. 1.2 - Prob. 39ECh. 1.2 - Prob. 40ECh. 1.2 - Prob. 41ECh. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.2 - Prob. 52ECh. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - Prob. 55ECh. 1.2 - Prob. 56ECh. 1.2 - Prob. 57ECh. 1.2 - Prob. 58ECh. 1.2 - Prob. 59ECh. 1.2 - Prob. 60ECh. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.3 - Prob. 1PQCh. 1.3 - Prob. 2PQCh. 1.3 - Prob. 3PQCh. 1.3 - Prob. 4PQCh. 1.3 - Prob. 5PQCh. 1.3 - Prob. 6PQCh. 1.3 - Prob. 1ECh. 1.3 - Prob. 2ECh. 1.3 - Prob. 3ECh. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.3 - Prob. 29ECh. 1.3 - Prob. 30ECh. 1.3 - Prob. 31ECh. 1.3 - Prob. 32ECh. 1.3 - Prob. 33ECh. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1.3 - Prob. 41ECh. 1.3 - Prob. 42ECh. 1.3 - Prob. 43ECh. 1.3 - Prob. 44ECh. 1.3 - Prob. 45ECh. 1.3 - Prob. 46ECh. 1.3 - Prob. 47ECh. 1.3 - Prob. 48ECh. 1.3 - Prob. 49ECh. 1.3 - Prob. 50ECh. 1.3 - Prob. 51ECh. 1.4 - Prob. 1PQCh. 1.4 - Prob. 2PQCh. 1.4 - Prob. 3PQCh. 1.4 - Prob. 4PQCh. 1.4 - Prob. 5PQCh. 1.4 - Prob. 6PQCh. 1.4 - Prob. 1ECh. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1.4 - Prob. 34ECh. 1.4 - Prob. 35ECh. 1.4 - Prob. 36ECh. 1.4 - Prob. 37ECh. 1.4 - Prob. 38ECh. 1.4 - Prob. 39ECh. 1.4 - Prob. 40ECh. 1.4 - Prob. 41ECh. 1.4 - Prob. 42ECh. 1.4 - Prob. 43ECh. 1.4 - Prob. 44ECh. 1.4 - Prob. 45ECh. 1.4 - Prob. 46ECh. 1.4 - Prob. 47ECh. 1.4 - Prob. 48ECh. 1.4 - Prob. 49ECh. 1.4 - Prob. 50ECh. 1.4 - Prob. 51ECh. 1.4 - Prob. 52ECh. 1.4 - Prob. 53ECh. 1.4 - Prob. 54ECh. 1.4 - Prob. 55ECh. 1.4 - Prob. 56ECh. 1.4 - Prob. 57ECh. 1.4 - Prob. 58ECh. 1.4 - Prob. 59ECh. 1.4 - Prob. 60ECh. 1.4 - Prob. 61ECh. 1.4 - Prob. 62ECh. 1.4 - Prob. 63ECh. 1.4 - Prob. 64ECh. 1.4 - Prob. 65ECh. 1.4 - Prob. 66ECh. 1.4 - Prob. 67ECh. 1.4 - Prob. 68ECh. 1.5 - Prob. 1PQCh. 1.5 - Prob. 2PQCh. 1.5 - Prob. 3PQCh. 1.5 - Prob. 4PQCh. 1.5 - Prob. 5PQCh. 1.5 - Prob. 6PQCh. 1.5 - Prob. 1ECh. 1.5 - Prob. 2ECh. 1.5 - Prob. 3ECh. 1.5 - Prob. 4ECh. 1.5 - Prob. 5ECh. 1.5 - Prob. 6ECh. 1.5 - Prob. 7ECh. 1.5 - Prob. 8ECh. 1.5 - Prob. 9ECh. 1.5 - Prob. 10ECh. 1.5 - Prob. 11ECh. 1.5 - Prob. 12ECh. 1.5 - Prob. 13ECh. 1.5 - Prob. 14ECh. 1.5 - Prob. 15ECh. 1.5 - Prob. 16ECh. 1.5 - Prob. 17ECh. 1.5 - Prob. 18ECh. 1.5 - Prob. 19ECh. 1.5 - Prob. 20ECh. 1.5 - Prob. 21ECh. 1.5 - Prob. 22ECh. 1.5 - Prob. 23ECh. 1.5 - Prob. 24ECh. 1.5 - Prob. 25ECh. 1.5 - Prob. 26ECh. 1.5 - Prob. 27ECh. 1.5 - Prob. 28ECh. 1.5 - Prob. 29ECh. 1.5 - Prob. 30ECh. 1.5 - Prob. 31ECh. 1.5 - Prob. 32ECh. 1.5 - Prob. 33ECh. 1.5 - Prob. 34ECh. 1.5 - Prob. 35ECh. 1.5 - Prob. 36ECh. 1.5 - Prob. 37ECh. 1.5 - Prob. 38ECh. 1.5 - Prob. 39ECh. 1.5 - Prob. 40ECh. 1.5 - Prob. 41ECh. 1.5 - Prob. 42ECh. 1.5 - Prob. 43ECh. 1.5 - Prob. 44ECh. 1.5 - Prob. 45ECh. 1.5 - Prob. 46ECh. 1.5 - Prob. 47ECh. 1.5 - Prob. 48ECh. 1.5 - Prob. 49ECh. 1.5 - Prob. 50ECh. 1.5 - Prob. 51ECh. 1.5 - Prob. 52ECh. 1.5 - Prob. 53ECh. 1.5 - Prob. 54ECh. 1.5 - Prob. 55ECh. 1.5 - Prob. 56ECh. 1.5 - Prob. 57ECh. 1.5 - Prob. 58ECh. 1.5 - Prob. 59ECh. 1.5 - Prob. 60ECh. 1.6 - Prob. 1PQCh. 1.6 - Prob. 2PQCh. 1.6 - Prob. 3PQCh. 1.6 - Prob. 4PQCh. 1.6 - Prob. 5PQCh. 1.6 - Prob. 6PQCh. 1.6 - Prob. 7PQCh. 1.6 - Prob. 8PQCh. 1.6 - Prob. 9PQCh. 1.6 - Prob. 1ECh. 1.6 - Prob. 2ECh. 1.6 - Prob. 3ECh. 1.6 - Prob. 4ECh. 1.6 - Prob. 5ECh. 1.6 - Prob. 6ECh. 1.6 - Prob. 7ECh. 1.6 - Prob. 8ECh. 1.6 - Prob. 9ECh. 1.6 - Prob. 10ECh. 1.6 - Prob. 11ECh. 1.6 - Prob. 12ECh. 1.6 - Prob. 13ECh. 1.6 - Prob. 14ECh. 1.6 - Prob. 15ECh. 1.6 - Prob. 16ECh. 1.6 - Prob. 17ECh. 1.6 - Prob. 18ECh. 1.6 - Prob. 19ECh. 1.6 - Prob. 20ECh. 1.6 - Prob. 21ECh. 1.6 - Prob. 22ECh. 1.6 - Prob. 23ECh. 1.6 - Prob. 24ECh. 1.6 - Prob. 25ECh. 1.6 - Prob. 26ECh. 1.6 - Prob. 27ECh. 1.6 - Prob. 28ECh. 1.6 - Prob. 29ECh. 1.6 - Prob. 30ECh. 1.6 - Prob. 31ECh. 1.6 - Prob. 32ECh. 1.6 - Prob. 33ECh. 1.6 - Prob. 34ECh. 1.6 - Prob. 35ECh. 1.6 - Prob. 36ECh. 1.6 - Prob. 37ECh. 1.6 - Prob. 38ECh. 1.6 - Prob. 39ECh. 1.6 - Prob. 40ECh. 1.6 - Prob. 41ECh. 1.6 - Prob. 42ECh. 1.6 - Prob. 43ECh. 1.6 - Prob. 44ECh. 1.6 - Prob. 45ECh. 1.6 - Prob. 46ECh. 1.6 - Prob. 47ECh. 1.6 - Prob. 48ECh. 1.6 - Prob. 49ECh. 1.6 - Prob. 50ECh. 1.6 - Prob. 51ECh. 1.6 - Prob. 52ECh. 1.6 - Prob. 53ECh. 1.7 - Prob. 1PQCh. 1.7 - Prob. 2PQCh. 1.7 - Prob. 3PQCh. 1.7 - Prob. 4PQCh. 1.7 - Prob. 1ECh. 1.7 - Prob. 2ECh. 1.7 - Prob. 3ECh. 1.7 - Prob. 4ECh. 1.7 - Prob. 5ECh. 1.7 - Prob. 6ECh. 1.7 - Prob. 7ECh. 1.7 - Prob. 8ECh. 1.7 - Prob. 9ECh. 1.7 - Prob. 10ECh. 1.7 - Prob. 11ECh. 1.7 - Prob. 12ECh. 1.7 - Prob. 13ECh. 1.7 - Prob. 14ECh. 1.7 - Prob. 15ECh. 1.7 - Prob. 16ECh. 1.7 - Prob. 17ECh. 1.7 - Prob. 18ECh. 1.7 - Prob. 19ECh. 1.7 - Prob. 20ECh. 1.7 - Prob. 21ECh. 1.7 - Prob. 22ECh. 1.7 - Prob. 23ECh. 1.7 - Prob. 24ECh. 1.7 - Prob. 25ECh. 1.7 - Prob. 26ECh. 1.7 - Prob. 27ECh. 1.7 - Prob. 28ECh. 1 - Prob. 1CRECh. 1 - Prob. 2CRECh. 1 - Prob. 3CRECh. 1 - Prob. 4CRECh. 1 - Prob. 5CRECh. 1 - Prob. 6CRECh. 1 - Prob. 7CRECh. 1 - Prob. 8CRECh. 1 - Prob. 9CRECh. 1 - Prob. 10CRECh. 1 - Prob. 11CRECh. 1 - Prob. 12CRECh. 1 - Prob. 13CRECh. 1 - Prob. 14CRECh. 1 - Prob. 15CRECh. 1 - Prob. 16CRECh. 1 - Prob. 17CRECh. 1 - Prob. 18CRECh. 1 - Prob. 19CRECh. 1 - Prob. 20CRECh. 1 - Prob. 21CRECh. 1 - Prob. 22CRECh. 1 - Prob. 23CRECh. 1 - Prob. 24CRECh. 1 - Prob. 25CRECh. 1 - Prob. 26CRECh. 1 - Prob. 27CRECh. 1 - Prob. 28CRECh. 1 - Prob. 29CRECh. 1 - Prob. 30CRECh. 1 - Prob. 31CRECh. 1 - Prob. 32CRECh. 1 - Prob. 33CRECh. 1 - Prob. 34CRECh. 1 - Prob. 35CRECh. 1 - Prob. 36CRECh. 1 - Prob. 37CRECh. 1 - Prob. 38CRECh. 1 - Prob. 39CRECh. 1 - Prob. 40CRECh. 1 - Prob. 41CRECh. 1 - Prob. 42CRECh. 1 - Prob. 43CRECh. 1 - Prob. 44CRECh. 1 - Prob. 45CRECh. 1 - Prob. 46CRECh. 1 - Prob. 47CRECh. 1 - Prob. 48CRECh. 1 - Prob. 49CRECh. 1 - Prob. 50CRECh. 1 - Prob. 51CRECh. 1 - Prob. 52CRECh. 1 - Prob. 53CRECh. 1 - Prob. 54CRECh. 1 - Prob. 55CRECh. 1 - Prob. 56CRECh. 1 - Prob. 57CRECh. 1 - Prob. 58CRECh. 1 - Prob. 59CRECh. 1 - Prob. 60CRECh. 1 - Prob. 61CRECh. 1 - Prob. 62CRECh. 1 - Prob. 63CRECh. 1 - Prob. 64CRECh. 1 - Prob. 65CRECh. 1 - Prob. 66CRE
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- Calculate these limits. If the limit is ∞ or -∞, write infinity or-infinity. If the limit does not exist, write DNE: Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator. 1. If the denominator does not go to 0, you should be able to right down the answer immediately. 2. If the denominator goes to 0, but the numerator does not, you will have to check the sign (±) of the quotient, from both sides if the limit is not one-sided. 3. If both the numerator and the denominator go to 0, you have to do the algebraic trick of rationalizing. So, group your limits into these three forms and work with them one group at a time. (a) lim t-pi/2 sint-√ sin 2t+14cos ² t 7 2 2 2cos t (b) lim sint + sin 2t+14cos = ∞ t-pi/2 2 2cos t (c) lim cost-√sin 2t+14cos² t = t-pi/2 2cos t (d) lim t→pi/2 cost+√ sin t + 14cos 2cos ² t = ∞ (e) lim sint-v sin 2 t + 14cos = 0 t-pi/2 (f) lim t-pi/2 sin t +√ sin 2sin 2 t 2 t + 14cos t 2sin t cost- (g)…arrow_forwardThink of this sheet of paper as the plane containing the vectors a = (1,1,0) and b = (2,0,0). Sketch the parallelogram P spanned by a and b. Which diagonal of P represents the vector a--b geometrically?arrow_forward(1) (14 points) Let a = (-2, 10, -4) and b = (3, 1, 1). (a) (4 points) Using the dot product determine the angle between a and b. (b) (2 points) Determine the cross product vector axb. (c) (4 points) Calculate the area of the parallelogram spanned by a and b. Justify your answer. 1arrow_forward
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