Single Variable Calculus: Early Transcendentals
8th Edition
ISBN: 9781305270336
Author: James Stewart
Publisher: Cengage Learning
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Chapter 9.3, Problem 36E
Find a function f such that f(3) = 2 and
![Chapter 9.3, Problem 36E, Find a function f such that f(3) = 2 and (t2+1)f(t)+[f(t)]2+1=0 t 1 [Hint: Use the addition formula](https://content.bartleby.com/tbms-images/9781305270336/Chapter-9/images/70336-9.3-36e-question-digital_image001.png)
[Hint: Use the addition formula for tan(x + y) on Reference Page 2.]
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EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
Chapter 9 Solutions
Single Variable Calculus: Early Transcendentals
Ch. 9.1 - Show that y=23ex+e2x is a solution of the...Ch. 9.1 - Prob. 2ECh. 9.1 - (a) For what values of r does the function y = erx...Ch. 9.1 - (a) For what values of k does the function y = cos...Ch. 9.1 - Which of the following functions are solutions of...Ch. 9.1 - (a) Show that every member of the family of...Ch. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
Ch. 9.1 - Explain why the functions with the given graphs...Ch. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Psychologists interested in learning theory study...Ch. 9.1 - Von Bertalanffys equation states that the rate of...Ch. 9.1 - Prob. 17ECh. 9.2 - A direction field for the differential equation y...Ch. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 19ECh. 9.2 - A direction field for a differential equation is...Ch. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Use Eulers method with step size 0.1 to estimate...Ch. 9.2 - Prob. 24ECh. 9.2 - Prob. 27ECh. 9.3 - Solve the differential equation. 1. dydx=3x2y2Ch. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Solve the differential equation. 5. (ey 1)y = 2 +...Ch. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Find an equation of the curve that passes through...Ch. 9.3 - Prob. 20ECh. 9.3 - Solve the differential equation y = x + y by...Ch. 9.3 - Solve the differential equation xy = y + xey/x by...Ch. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Prob. 29ECh. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - An integral equation is an equation that contains...Ch. 9.3 - Prob. 35ECh. 9.3 - Find a function f such that f(3) = 2 and...Ch. 9.3 - Solve the initial-value problem in Exercise 9.2.27...Ch. 9.3 - Prob. 38ECh. 9.3 - In Exercise 9.1.15 we formulated a model for...Ch. 9.3 - Prob. 40ECh. 9.3 - Prob. 41ECh. 9.3 - A sphere with radius 1 m has temperature 15C. It...Ch. 9.3 - A glucose solution is administered intravenously...Ch. 9.3 - A certain small country has 10 billion in paper...Ch. 9.3 - Prob. 45ECh. 9.3 - Prob. 46ECh. 9.3 - Prob. 47ECh. 9.3 - Prob. 48ECh. 9.3 - Prob. 49ECh. 9.3 - Prob. 50ECh. 9.3 - Prob. 51ECh. 9.3 - Prob. 52ECh. 9.3 - Prob. 54ECh. 9.4 - Prob. 1ECh. 9.4 - A population grows according to the given logistic...Ch. 9.4 - Prob. 3ECh. 9.4 - The Pacific halibut fishery has been modeled by...Ch. 9.4 - Suppose a population P(t) satisfies...Ch. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 9.4 - Biologists stocked a lake with 400 fish and...Ch. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Let c be a positive number. A differential...Ch. 9.4 - There is considerable evidence to support the...Ch. 9.4 - Another model for a growth function for a limited...Ch. 9.4 - Prob. 23ECh. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - Prob. 6ECh. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Solve the differential equation. 13....Ch. 9.5 - Solve the differential equation. 14....Ch. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - Use the method of Exercise 23 to solve the...Ch. 9.5 - Prob. 26ECh. 9.5 - In the circuit shown in Figure 4, a battery...Ch. 9.5 - In the circuit shown in Figure 4, a generator...Ch. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Let P(t) be the performance level of someone...Ch. 9.5 - Prob. 32ECh. 9.5 - In Section 9.3 we looked at mixing problems in...Ch. 9.5 - A tank with a capacity of 400 L is full of a...Ch. 9.5 - Prob. 35ECh. 9.5 - Prob. 36ECh. 9.5 - Prob. 37ECh. 9.5 - Prob. 38ECh. 9.6 - Prob. 1ECh. 9.6 - Each system of differential equations is a model...Ch. 9.6 - Prob. 3ECh. 9.6 - Lynx eat snowshoe hares and snowshoe hares eat...Ch. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 10ECh. 9.6 - In Example 1 we used Lotka-Volterra equations to...Ch. 9 - Prob. 1RCCCh. 9 - What can you say about the solutions of the...Ch. 9 - Prob. 3RCCCh. 9 - Prob. 4RCCCh. 9 - Prob. 5RCCCh. 9 - Prob. 6RCCCh. 9 - Prob. 7RCCCh. 9 - Prob. 8RCCCh. 9 - Prob. 9RCCCh. 9 - Determine whether the statement is true or false....Ch. 9 - Prob. 2RQCh. 9 - Determine whether the statement is true or false....Ch. 9 - Prob. 4RQCh. 9 - Prob. 5RQCh. 9 - Determine whether the statement is true or false....Ch. 9 - Prob. 7RQCh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Solve the differential equation. 5. y = xesin x y...Ch. 9 - Prob. 6RECh. 9 - Solve the differential equation. 7. 2yey2y=2x+3xCh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - A tank contains 100 L of pure water. Brine that...Ch. 9 - One model for the spread of an epidemic is that...Ch. 9 - The Brentano-Stevens Law in psychology models the...Ch. 9 - The transport of a substance across a capillary...Ch. 9 - Populations of birds and insects are modeled by...Ch. 9 - Prob. 23RECh. 9 - Barbara weighs 60 kg and is on a diet of 1600...Ch. 9 - Prob. 1PCh. 9 - Prob. 2PCh. 9 - Prob. 3PCh. 9 - Find all functions f that satisfy the equation...Ch. 9 - Prob. 5PCh. 9 - Prob. 6PCh. 9 - Prob. 7PCh. 9 - Snow began to fall during the morning of February...Ch. 9 - Prob. 9PCh. 9 - Prob. 10PCh. 9 - Prob. 11PCh. 9 - Prob. 12PCh. 9 - Prob. 13PCh. 9 - Prob. 14PCh. 9 - Prob. 15P
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