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Calculus with Applications (11th Edition)
11th Edition
ISBN: 9780321979421
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Question
Chapter 1.1, Problem 52E
To determine
To sketch: The graph of the equation
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Students have asked these similar questions
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
Macbook Pro
Evaluate the integral using integration by parts.
Sx² cos
(9x) dx
Let f be defined as follows.
y = f(x) = x² - 5x
(a) Find the average rate of change of y with respect to x in the following intervals.
from x = 4 to x = 5
from x = 4 to x = 4.5
from x = 4 to x = 4.1
(b) Find the (instantaneous) rate of change of y at x = 4.
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Chapter 1 Solutions
Calculus with Applications (11th Edition)
Ch. 1.1 - YOUR TURN 1 Find the slope of the line through (1,...Ch. 1.1 - YOUR TURN 2 Find the equation of the line with...Ch. 1.1 - YOUR TURN 3 Find the slope of the line whose...Ch. 1.1 - YOUR TURN 4 Find the equation of the line through...Ch. 1.1 - Prob. 5YTCh. 1.1 - YOUR TURN 6 Find the equation of the line passing...Ch. 1.1 - W1. Evaluate . (Sec. R.1)
Ch. 1.1 - Solve each equation for y. (Sec. R.4)
W2. y − (−3)...Ch. 1.1 - Solve each equation for y. (Sec. R.4)
W3.
Ch. 1.1 - Prob. 4WE
Ch. 1.1 - Find the slope of each line.
1. Through (4, 5) and...Ch. 1.1 - Prob. 2ECh. 1.1 - Find the slope of each line.
3. Through (8, 4) and...Ch. 1.1 - Prob. 4ECh. 1.1 - Prob. 5ECh. 1.1 - Find the slope of each line.
6. y = 3x − 2
Ch. 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 - Find the slope of each line.
13. A line parallel...Ch. 1.1 - Find the slope of each line.
14. A line...Ch. 1.1 - In Exercises 15–24, find an equation in...Ch. 1.1 - Prob. 16ECh. 1.1 - Prob. 17ECh. 1.1 - In Exercises 15–24, find an equation in...Ch. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - In Exercises 15–24, find an equation in...Ch. 1.1 - In Exercises 15–24, find an equation in...Ch. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - In Exercises 25–34, find an equation for each line...Ch. 1.1 - Prob. 35ECh. 1.1 - Prob. 36ECh. 1.1 - Prob. 37ECh. 1.1 - 38. Use slopes to show that the square with...Ch. 1.1 - Prob. 39ECh. 1.1 - For the lines in Exercises 39 and 40, which of the...Ch. 1.1 - Prob. 41ECh. 1.1 - In Exercises 41 and 42, estimate the slope of the...Ch. 1.1 - 43. To show that two perpendicular lines, neither...Ch. 1.1 - Prob. 44ECh. 1.1 - Prob. 45ECh. 1.1 - Graph each equation.
46. y = 4x + 5
Ch. 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 - Graph each equation.
59. x + 4y = 0
Ch. 1.1 - Prob. 60ECh. 1.1 - Prob. 61ECh. 1.1 - 62. Cost The total cost for a bakery to produce...Ch. 1.1 - Prob. 63ECh. 1.1 - Prob. 64ECh. 1.1 - Prob. 65ECh. 1.1 - Life Sciences
66. HIV Infection The time interval...Ch. 1.1 - Prob. 67ECh. 1.1 - Prob. 68ECh. 1.1 - Prob. 69ECh. 1.1 - Prob. 70ECh. 1.1 - 71. Immigration In 1950, there were 249,187...Ch. 1.1 - 72. Marriage The following table lists the U.S....Ch. 1.1 - Prob. 73ECh. 1.1 - Prob. 74ECh. 1.1 - Prob. 75ECh. 1.2 - Prob. 1YTCh. 1.2 - Prob. 2YTCh. 1.2 - Prob. 3YTCh. 1.2 - YOUR TURN 4 Repeat Example 5, using a marginal...Ch. 1.2 - Prob. 5YTCh. 1.2 - Prob. 6YTCh. 1.2 - Prob. 1WECh. 1.2 - Prob. 2WECh. 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 - In Exercises 11–14, decide whether the statement...Ch. 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 - Assume that each situation can be expressed as a...Ch. 1.2 - Prob. 24ECh. 1.2 - Prob. 25ECh. 1.2 - Prob. 26ECh. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - 29. Supply and Demand Let the supply and demand...Ch. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - Prob. 33ECh. 1.2 - 34. Break-Even Analysis To produce x units of a...Ch. 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 - 43. Break-Even Analysis Suppose that the fixed...Ch. 1.2 - Prob. 44ECh. 1.2 - Life Sciences
45. Deer Ticks Deer ticks are of...Ch. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.3 - YOUR TURN 1 Calculate the least squares line for...Ch. 1.3 - Prob. 2YTCh. 1.3 - Prob. 1ECh. 1.3 - Prob. 2ECh. 1.3 - Prob. 3ECh. 1.3 - The following problem is reprinted from the...Ch. 1.3 - 5. Consider the following table of...Ch. 1.3 - 6. Consider the following table of...Ch. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - 9. The formulas for the least squares line were...Ch. 1.3 - 10. Consumer Durable Goods The total value of...Ch. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - 14. Consumer Credit The total amount of consumer...Ch. 1.3 - 15. Mean Earnings The mean earnings (in dollars)...Ch. 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. 29ECh. 1 - Prob. 1RECh. 1 - Determine whether each statement is true or false,...Ch. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - Prob. 40RECh. 1 - Prob. 41RECh. 1 - Prob. 42RECh. 1 - Prob. 43RECh. 1 - Prob. 44RECh. 1 - Prob. 45RECh. 1 - 46. U.S. Exports to China U.S. exports to China...Ch. 1 - Prob. 47RECh. 1 - Prob. 48RECh. 1 - Prob. 49RECh. 1 - Prob. 50RECh. 1 - Prob. 51RECh. 1 - Prob. 52RECh. 1 - Prob. 53RECh. 1 - Prob. 54RECh. 1 - Prob. 55RECh. 1 - Prob. 56RECh. 1 - Prob. 57RECh. 1 - Prob. 58RECh. 1 - Prob. 59RECh. 1 - Life Sciences
60. World Health In general, people...Ch. 1 - Prob. 61RECh. 1 - Prob. 62RECh. 1 - Prob. 63RECh. 1 - Prob. 65RE
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