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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
8th Edition
ISBN: 9781305279148
Author: Stewart, James, St. Andre, Richard
Publisher: Cengage Learning
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Question
Chapter 3.10, Problem 3PT
To determine
To choose: The appropriate option for the linearization of
Expert Solution & Answer
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Students have asked these similar questions
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)
Macbook Pro
Evaluate the integral using integration by parts.
Sx² cos
(9x) dx
Chapter 3 Solutions
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Ch. 3.1 - Prob. 1PTCh. 3.1 - Prob. 2PTCh. 3.1 - Prob. 3PTCh. 3.1 - Prob. 4PTCh. 3.1 - Prob. 5PTCh. 3.1 - Prob. 6PTCh. 3.2 - Prob. 1PTCh. 3.2 - Prob. 2PTCh. 3.2 - Prob. 3PTCh. 3.2 - Prob. 4PT
Ch. 3.3 - Prob. 1PTCh. 3.3 - Prob. 2PTCh. 3.3 - Prob. 3PTCh. 3.3 - Prob. 4PTCh. 3.3 - Prob. 5PTCh. 3.3 - Prob. 6PTCh. 3.4 - Prob. 1PTCh. 3.4 - Prob. 2PTCh. 3.4 - Prob. 3PTCh. 3.4 - Prob. 4PTCh. 3.4 - Prob. 5PTCh. 3.4 - Prob. 6PTCh. 3.4 - Prob. 7PTCh. 3.5 - Prob. 1PTCh. 3.5 - Prob. 2PTCh. 3.5 - Prob. 3PTCh. 3.5 - Prob. 4PTCh. 3.5 - Prob. 5PTCh. 3.5 - Prob. 6PTCh. 3.6 - Prob. 1PTCh. 3.6 - Prob. 2PTCh. 3.6 - Prob. 3PTCh. 3.6 - Prob. 4PTCh. 3.6 - Prob. 5PTCh. 3.7 - Prob. 1PTCh. 3.7 - Prob. 2PTCh. 3.7 - Prob. 3PTCh. 3.7 - Prob. 4PTCh. 3.8 - Prob. 1PTCh. 3.8 - A bacteria culture starts with 50 organisms and...Ch. 3.8 - Prob. 3PTCh. 3.9 - A right triangle has one leg with constant length...Ch. 3.9 - Prob. 2PTCh. 3.10 - Prob. 1PTCh. 3.10 - Prob. 2PTCh. 3.10 - Prob. 3PTCh. 3.10 - Prob. 4PTCh. 3.11 - Prob. 1PTCh. 3.11 - Prob. 2PTCh. 3.11 - Prob. 3PTCh. 3.11 - Prob. 4PTCh. 3.11 - Prob. 5PT
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- 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. Need Help? Read It Master Itarrow_forwardVelocity of a Ball Thrown into the Air The position function of an object moving along a straight line is given by s = f(t). The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a. A ball is thrown straight up with an initial velocity of 128 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 128t - 16t². (a) What is the average velocity of the ball over the following time intervals? [3,4] [3, 3.5] [3, 3.1] ft/sec ft/sec ft/sec (b) What is the instantaneous velocity at time t = 3? ft/sec (c) What is the instantaneous velocity at time t = 7? ft/sec Is the ball rising or falling at this time? O rising falling (d) When will the ball hit the ground? t = sec Need Help? Read It Watch Itarrow_forwardpractice problem please help!arrow_forward
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