EBK CALCULUS: AN APPLIED APPROACH
10th Edition
ISBN: 8220101426222
Author: Larson
Publisher: CENGAGE L
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Textbook Question
Chapter 11.4, Problem 27E
Chemical Mixture A 100-gallon tank is full of a solution containing 25 pounds of a concentrate. Starting at time
(a) Find the amount Q of the concentrate in the solution as a function of t by solving the
(b) Find the time required for the amount of concentrate in the tank to reach 15 pounds.
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Students have asked these similar questions
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(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)
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Chapter 11 Solutions
EBK CALCULUS: AN APPLIED APPROACH
Ch. 11.1 - Checkpoint 1 Worked-out solution available at...Ch. 11.1 - Prob. 2CPCh. 11.1 - Prob. 3CPCh. 11.1 - Prob. 4CPCh. 11.1 - Prob. 1SWUCh. 11.1 - Prob. 2SWUCh. 11.1 - Prob. 3SWUCh. 11.1 - Prob. 4SWUCh. 11.1 - Prob. 5SWUCh. 11.1 - Prob. 6SWU
Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Verifying Solutions In Exercises 1-12, verify the...Ch. 11.1 - Prob. 10ECh. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Determining Solutions In Exercises 1316, determine...Ch. 11.1 - Prob. 16ECh. 11.1 - Determining Solutions In Exercises 1720, determine...Ch. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Investment The rate of growth of an investment is...Ch. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.2 - Checkpoint 1 Worked-out solution available at...Ch. 11.2 - Prob. 2CPCh. 11.2 - Prob. 3CPCh. 11.2 - Prob. 4CPCh. 11.2 - Prob. 5CPCh. 11.2 - Prob. 6CPCh. 11.2 - Prob. 1SWUCh. 11.2 - Prob. 2SWUCh. 11.2 - Prob. 3SWUCh. 11.2 - Prob. 4SWUCh. 11.2 - Prob. 5SWUCh. 11.2 - Prob. 6SWUCh. 11.2 - Prob. 7SWUCh. 11.2 - Prob. 8SWUCh. 11.2 - Prob. 9SWUCh. 11.2 - Prob. 10SWUCh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 33ECh. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 35ECh. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Solve the differential equation. Weight Gain A...Ch. 11.2 - Prob. 1QYCh. 11.2 - Prob. 2QYCh. 11.2 - Prob. 3QYCh. 11.2 - Prob. 4QYCh. 11.2 - Prob. 5QYCh. 11.2 - Prob. 6QYCh. 11.2 - Prob. 7QYCh. 11.2 - Prob. 8QYCh. 11.2 - Prob. 9QYCh. 11.2 - Prob. 10QYCh. 11.2 - Prob. 11QYCh. 11.2 - Prob. 12QYCh. 11.2 - Prob. 13QYCh. 11.2 - Prob. 14QYCh. 11.2 - Prob. 15QYCh. 11.2 - Ignoring resistance, a sailboat starting from rest...Ch. 11.3 - Checkpoint 1 Worked-out solution available at...Ch. 11.3 - Prob. 2CPCh. 11.3 - Prob. 3CPCh. 11.3 - Prob. 1SWUCh. 11.3 - Prob. 2SWUCh. 11.3 - Prob. 3SWUCh. 11.3 - Prob. 4SWUCh. 11.3 - Prob. 5SWUCh. 11.3 - Prob. 6SWUCh. 11.3 - Prob. 7SWUCh. 11.3 - Prob. 8SWUCh. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - Prob. 10SWUCh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 10ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 17ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Using Two Methods In Exercises 19-22, solve for y...Ch. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Vertical Motion A falling object encounters air...Ch. 11.3 - Velocity A booster rocket carrying an observation...Ch. 11.3 - Learning Curve The management at a medical supply...Ch. 11.3 - Investment Let A he the amount in a fund earning...Ch. 11.4 - Prob. 1CPCh. 11.4 - Prob. 2CPCh. 11.4 - Checkpoint 3 Worked-out solution available at...Ch. 11.4 - Prob. 4CPCh. 11.4 - Checkpoint 5 Worked-out solution available at...Ch. 11.4 - Prob. 1SWUCh. 11.4 - Prob. 2SWUCh. 11.4 - Prob. 3SWUCh. 11.4 - Prob. 4SWUCh. 11.4 - Prob. 5SWUCh. 11.4 - Prob. 6SWUCh. 11.4 - Prob. 7SWUCh. 11.4 - Prob. 8SWUCh. 11.4 - Prob. 9SWUCh. 11.4 - Prob. 10SWUCh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Advertising Awareness In Exercises 3 and 4, use...Ch. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Chemistry A wet towel hung from a clothesline to...Ch. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Biology A population of eight beavers has been...Ch. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Chemical Mixture A 100-gallon tank is full of a...Ch. 11.4 - Chemical Mixture A 200-gallon tank is half full of...Ch. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Prob. 36ECh. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11 - Prob. 1RECh. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Finding a Particular Solution In Exercises 15 and...Ch. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Prob. 40RECh. 11 - Prob. 41RECh. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Prob. 43RECh. 11 - Prob. 44RECh. 11 - Prob. 45RECh. 11 - Prob. 46RECh. 11 - Prob. 47RECh. 11 - Prob. 48RECh. 11 - Prob. 49RECh. 11 - Prob. 50RECh. 11 - Prob. 51RECh. 11 - Prob. 52RECh. 11 - Prob. 53RECh. 11 - Prob. 54RECh. 11 - Prob. 55RECh. 11 - Prob. 56RECh. 11 - Solving a Linear Differential Equation In...Ch. 11 - Prob. 58RECh. 11 - Prob. 59RECh. 11 - Prob. 60RECh. 11 - Prob. 61RECh. 11 - Prob. 62RECh. 11 - Prob. 63RECh. 11 - Prob. 64RECh. 11 - Prob. 65RECh. 11 - Prob. 66RECh. 11 - Safety Assume the rate of change per hour in the...Ch. 11 - Prob. 68RECh. 11 - Prob. 69RECh. 11 - Prob. 70RECh. 11 - Prob. 71RECh. 11 - Prob. 72RECh. 11 - Prob. 73RECh. 11 - Prob. 74RECh. 11 - Prob. 75RECh. 11 - Chemical Mixture A tank contains 30 gallons of a...Ch. 11 - Chemical Mixture A tank contains 20 gallons of a...Ch. 11 - Prob. 1TYSCh. 11 - Prob. 2TYSCh. 11 - Prob. 3TYSCh. 11 - Prob. 4TYSCh. 11 - Prob. 5TYSCh. 11 - Prob. 6TYSCh. 11 - Prob. 7TYSCh. 11 - Prob. 8TYSCh. 11 - Prob. 9TYSCh. 11 - Prob. 10TYSCh. 11 - Prob. 11TYSCh. 11 - A lamb that weighs 10 pounds at birth gains weight...Ch. 11 - Prob. 13TYS
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