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 12.3, Problem 2E
To determine
Findthedot product of the given
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48. The domain of f
y=f'(x)
x
1
2
(=
x<0
x<0
= f(x)
possible.
Group Activity In Exercises 49 and 50, do the following.
(a) Find the absolute extrema of f and where they occur.
(b) Find any points of inflection.
(c) Sketch a possible graph of f.
49. f is continuous on [0,3] and satisfies the following.
X
0
1
2
3
f
0
2
0
-2
f'
3
0
does not exist
-3
f"
0
-1
does not exist
0
ve
tes where
X
0 < x <1
1< x <2
2
Numerically estimate the value of limx→2+x3−83x−9, rounded correctly to one decimal place.
In the provided table below, you must enter your answers rounded exactly to the correct number of decimals, based on the Numerical Conventions for MATH1044 (see lecture notes 1.3
Actions
page 3). If there are more rows provided in the table than you need, enter NA for those output values in the table that should not be used.
x→2+
x3−83x−9
2.1
2.01
2.001
2.0001
2.00001
2.000001
Find the general solution of the given differential equation.
(1+x)dy/dx - xy = x +x2
Chapter 12 Solutions
Loose-leaf Version For Calculus: Early Transcendentals
Ch. 12.1 - Prob. 1PQCh. 12.1 - Prob. 2PQCh. 12.1 - Prob. 3PQCh. 12.1 - Prob. 4PQCh. 12.1 - Prob. 5PQCh. 12.1 - Prob. 6PQCh. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4E
Ch. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.1 - Prob. 10ECh. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Prob. 32ECh. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - Prob. 37ECh. 12.1 - Prob. 38ECh. 12.1 - Prob. 39ECh. 12.1 - Prob. 40ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - Prob. 43ECh. 12.1 - Prob. 44ECh. 12.1 - Prob. 45ECh. 12.1 - Prob. 46ECh. 12.1 - Prob. 47ECh. 12.1 - Prob. 48ECh. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Prob. 53ECh. 12.1 - Prob. 54ECh. 12.1 - 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Prob. 88ECh. 12.3 - Prob. 89ECh. 12.3 - Prob. 90ECh. 12.3 - Prob. 91ECh. 12.3 - Prob. 92ECh. 12.3 - Prob. 93ECh. 12.3 - Prob. 94ECh. 12.3 - Prob. 95ECh. 12.3 - Prob. 96ECh. 12.3 - Prob. 97ECh. 12.3 - Prob. 98ECh. 12.3 - Prob. 99ECh. 12.3 - Prob. 100ECh. 12.3 - Prob. 101ECh. 12.3 - Prob. 102ECh. 12.3 - Prob. 103ECh. 12.3 - Prob. 104ECh. 12.3 - Prob. 105ECh. 12.4 - Prob. 1PQCh. 12.4 - Prob. 2PQCh. 12.4 - Prob. 3PQCh. 12.4 - Prob. 4PQCh. 12.4 - Prob. 5PQCh. 12.4 - Prob. 6PQCh. 12.4 - Prob. 7PQCh. 12.4 - Prob. 8PQCh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - Prob. 13ECh. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - Prob. 35ECh. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.4 - Prob. 38ECh. 12.4 - Prob. 39ECh. 12.4 - Prob. 40ECh. 12.4 - Prob. 41ECh. 12.4 - Prob. 42ECh. 12.4 - Prob. 43ECh. 12.4 - Prob. 44ECh. 12.4 - Prob. 45ECh. 12.4 - Prob. 46ECh. 12.4 - Prob. 47ECh. 12.4 - Prob. 48ECh. 12.4 - Prob. 49ECh. 12.4 - Prob. 50ECh. 12.4 - Prob. 51ECh. 12.4 - Prob. 52ECh. 12.4 - Prob. 53ECh. 12.4 - Prob. 54ECh. 12.4 - Prob. 55ECh. 12.4 - Prob. 56ECh. 12.4 - Prob. 57ECh. 12.4 - Prob. 58ECh. 12.4 - Prob. 59ECh. 12.4 - Prob. 60ECh. 12.4 - Prob. 61ECh. 12.4 - Prob. 62ECh. 12.4 - Prob. 63ECh. 12.4 - Prob. 64ECh. 12.4 - Prob. 65ECh. 12.4 - Prob. 66ECh. 12.4 - Prob. 67ECh. 12.4 - Prob. 68ECh. 12.4 - Prob. 69ECh. 12.4 - Prob. 70ECh. 12.4 - Prob. 71ECh. 12.4 - Prob. 72ECh. 12.4 - Prob. 73ECh. 12.4 - Prob. 74ECh. 12.4 - Prob. 75ECh. 12.4 - Prob. 76ECh. 12.4 - Prob. 77ECh. 12.4 - Prob. 78ECh. 12.4 - Prob. 79ECh. 12.4 - Prob. 80ECh. 12.4 - Prob. 81ECh. 12.4 - Prob. 82ECh. 12.4 - Prob. 83ECh. 12.5 - Prob. 1PQCh. 12.5 - Prob. 2PQCh. 12.5 - Prob. 3PQCh. 12.5 - Prob. 4PQCh. 12.5 - Prob. 5PQCh. 12.5 - Prob. 6PQCh. 12.5 - Prob. 1ECh. 12.5 - Prob. 2ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - Prob. 9ECh. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - Prob. 13ECh. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Prob. 22ECh. 12.5 - Prob. 23ECh. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - Prob. 26ECh. 12.5 - Prob. 27ECh. 12.5 - Prob. 28ECh. 12.5 - Prob. 29ECh. 12.5 - Prob. 30ECh. 12.5 - Prob. 31ECh. 12.5 - Prob. 32ECh. 12.5 - Prob. 33ECh. 12.5 - Prob. 34ECh. 12.5 - Prob. 35ECh. 12.5 - Prob. 36ECh. 12.5 - Prob. 37ECh. 12.5 - Prob. 38ECh. 12.5 - Prob. 39ECh. 12.5 - Prob. 40ECh. 12.5 - Prob. 41ECh. 12.5 - Prob. 42ECh. 12.5 - Prob. 43ECh. 12.5 - Prob. 44ECh. 12.5 - Prob. 45ECh. 12.5 - Prob. 46ECh. 12.5 - Prob. 47ECh. 12.5 - Prob. 48ECh. 12.5 - Prob. 49ECh. 12.5 - Prob. 50ECh. 12.5 - Prob. 51ECh. 12.5 - Prob. 52ECh. 12.5 - Prob. 53ECh. 12.5 - Prob. 54ECh. 12.5 - Prob. 55ECh. 12.5 - Prob. 56ECh. 12.5 - Prob. 57ECh. 12.5 - Prob. 58ECh. 12.5 - Prob. 59ECh. 12.5 - Prob. 60ECh. 12.5 - Prob. 61ECh. 12.5 - Prob. 62ECh. 12.5 - Prob. 63ECh. 12.5 - Prob. 64ECh. 12.5 - Prob. 65ECh. 12.5 - Prob. 66ECh. 12.5 - Prob. 67ECh. 12.5 - Prob. 68ECh. 12.5 - Prob. 69ECh. 12.5 - Prob. 70ECh. 12.5 - Prob. 71ECh. 12.5 - Prob. 72ECh. 12.5 - Prob. 73ECh. 12.5 - Prob. 74ECh. 12.5 - Prob. 75ECh. 12.5 - Prob. 76ECh. 12.5 - Prob. 77ECh. 12.5 - Prob. 78ECh. 12.5 - Prob. 79ECh. 12.5 - Prob. 80ECh. 12.6 - Prob. 1PQCh. 12.6 - Prob. 2PQCh. 12.6 - Prob. 3PQCh. 12.6 - Prob. 4PQCh. 12.6 - Prob. 5PQCh. 12.6 - Prob. 6PQCh. 12.6 - Prob. 1ECh. 12.6 - Prob. 2ECh. 12.6 - Prob. 3ECh. 12.6 - Prob. 4ECh. 12.6 - Prob. 5ECh. 12.6 - Prob. 6ECh. 12.6 - Prob. 7ECh. 12.6 - Prob. 8ECh. 12.6 - Prob. 9ECh. 12.6 - Prob. 10ECh. 12.6 - Prob. 11ECh. 12.6 - Prob. 12ECh. 12.6 - Prob. 13ECh. 12.6 - Prob. 14ECh. 12.6 - Prob. 15ECh. 12.6 - Prob. 16ECh. 12.6 - Prob. 17ECh. 12.6 - Prob. 18ECh. 12.6 - Prob. 19ECh. 12.6 - Prob. 20ECh. 12.6 - Prob. 21ECh. 12.6 - Prob. 22ECh. 12.6 - Prob. 23ECh. 12.6 - Prob. 24ECh. 12.6 - Prob. 25ECh. 12.6 - Prob. 26ECh. 12.6 - Prob. 27ECh. 12.6 - Prob. 28ECh. 12.6 - Prob. 29ECh. 12.6 - Prob. 30ECh. 12.6 - Prob. 31ECh. 12.6 - Prob. 32ECh. 12.6 - Prob. 33ECh. 12.6 - Prob. 34ECh. 12.6 - Prob. 35ECh. 12.6 - Prob. 36ECh. 12.6 - Prob. 37ECh. 12.6 - Prob. 38ECh. 12.6 - Prob. 39ECh. 12.6 - Prob. 40ECh. 12.6 - Prob. 41ECh. 12.6 - Prob. 42ECh. 12.6 - Prob. 43ECh. 12.6 - Prob. 44ECh. 12.6 - Prob. 45ECh. 12.6 - Prob. 46ECh. 12.6 - Prob. 47ECh. 12.6 - Prob. 48ECh. 12.6 - Prob. 49ECh. 12.6 - Prob. 50ECh. 12.6 - Prob. 51ECh. 12.6 - Prob. 52ECh. 12.6 - Prob. 53ECh. 12.7 - Prob. 1PQCh. 12.7 - Prob. 2PQCh. 12.7 - Prob. 3PQCh. 12.7 - Prob. 4PQCh. 12.7 - Prob. 5PQCh. 12.7 - Prob. 1ECh. 12.7 - Prob. 2ECh. 12.7 - Prob. 3ECh. 12.7 - Prob. 4ECh. 12.7 - Prob. 5ECh. 12.7 - Prob. 6ECh. 12.7 - Prob. 7ECh. 12.7 - Prob. 8ECh. 12.7 - Prob. 9ECh. 12.7 - Prob. 10ECh. 12.7 - Prob. 11ECh. 12.7 - Prob. 12ECh. 12.7 - Prob. 13ECh. 12.7 - Prob. 14ECh. 12.7 - Prob. 15ECh. 12.7 - Prob. 16ECh. 12.7 - Prob. 17ECh. 12.7 - Prob. 18ECh. 12.7 - Prob. 19ECh. 12.7 - Prob. 20ECh. 12.7 - Prob. 21ECh. 12.7 - Prob. 22ECh. 12.7 - Prob. 23ECh. 12.7 - Prob. 24ECh. 12.7 - Prob. 25ECh. 12.7 - Prob. 26ECh. 12.7 - Prob. 27ECh. 12.7 - Prob. 28ECh. 12.7 - Prob. 29ECh. 12.7 - Prob. 30ECh. 12.7 - Prob. 31ECh. 12.7 - Prob. 32ECh. 12.7 - Prob. 33ECh. 12.7 - Prob. 34ECh. 12.7 - Prob. 35ECh. 12.7 - Prob. 36ECh. 12.7 - Prob. 37ECh. 12.7 - Prob. 38ECh. 12.7 - Prob. 39ECh. 12.7 - Prob. 40ECh. 12.7 - Prob. 41ECh. 12.7 - Prob. 42ECh. 12.7 - Prob. 43ECh. 12.7 - Prob. 44ECh. 12.7 - Prob. 45ECh. 12.7 - Prob. 46ECh. 12.7 - 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- A function is defined on the interval (-π/2,π/2) by this multipart rule: if -π/2 < x < 0 f(x) = a if x=0 31-tan x +31-cot x if 0 < x < π/2 Here, a and b are constants. Find a and b so that the function f(x) is continuous at x=0. a= b= 3arrow_forwardUse the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = (x + 4x4) 5, a = -1 lim f(x) X--1 = lim x+4x X--1 lim X-1 4 x+4x 5 ))" 5 )) by the power law by the sum law lim (x) + lim X--1 4 4x X-1 -(0,00+( Find f(-1). f(-1)=243 lim (x) + -1 +4 35 4 ([ ) lim (x4) 5 x-1 Thus, by the definition of continuity, f is continuous at a = -1. by the multiple constant law by the direct substitution propertyarrow_forward1. Compute Lo F⚫dr, where and C is defined by F(x, y) = (x² + y)i + (y − x)j r(t) = (12t)i + (1 − 4t + 4t²)j from the point (1, 1) to the origin.arrow_forward
- 2. Consider the vector force: F(x, y, z) = 2xye²i + (x²e² + y)j + (x²ye² — z)k. (A) [80%] Show that F satisfies the conditions for a conservative vector field, and find a potential function (x, y, z) for F. Remark: To find o, you must use the method explained in the lecture. (B) [20%] Use the Fundamental Theorem for Line Integrals to compute the work done by F on an object moves along any path from (0,1,2) to (2, 1, -8).arrow_forwardhelp pleasearrow_forwardIn each of Problems 1 through 4, draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t → ∞. If this behavior depends on the initial value of y at t = 0, describe the dependency.1. y′ = 3 − 2yarrow_forward
- B 2- The figure gives four points and some corresponding rays in the xy-plane. Which of the following is true? A B Angle COB is in standard position with initial ray OB and terminal ray OC. Angle COB is in standard position with initial ray OC and terminal ray OB. C Angle DOB is in standard position with initial ray OB and terminal ray OD. D Angle DOB is in standard position with initial ray OD and terminal ray OB.arrow_forwardtemperature in degrees Fahrenheit, n hours since midnight. 5. The temperature was recorded at several times during the day. Function T gives the Here is a graph for this function. To 29uis a. Describe the overall trend of temperature throughout the day. temperature (Fahrenheit) 40 50 50 60 60 70 5 10 15 20 25 time of day b. Based on the graph, did the temperature change more quickly between 10:00 a.m. and noon, or between 8:00 p.m. and 10:00 p.m.? Explain how you know. (From Unit 4, Lesson 7.) 6. Explain why this graph does not represent a function. (From Unit 4, Lesson 8.)arrow_forwardFind the area of the shaded region. (a) 5- y 3 2- (1,4) (5,0) 1 3 4 5 6 (b) 3 y 2 Decide whether the problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. STEP 1: Consider the figure in part (a). Since this region is simply a triangle, you may use precalculus methods to solve this part of the problem. First determine the height of the triangle and the length of the triangle's base. height 4 units units base 5 STEP 2: Compute the area of the triangle by employing a formula from precalculus, thus finding the area of the shaded region in part (a). 10 square units STEP 3: Consider the figure in part (b). Since this region is defined by a complicated curve, the problem seems to require calculus. Find an approximation of the shaded region by using a graphical approach. (Hint: Treat the shaded regi as…arrow_forward
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