Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
14th Edition
ISBN: 9780134668574
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker
Publisher: PEARSON
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Textbook Question
Chapter 8, Problem 31RE
In Problems 29–31, graph each function on a graphing calculator set in radian mode.
31. y = 3 –2 cos πx; 0 ≤ x ≤ 6, 0 ≤ y ≤ 5
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2. a. arctan(-1)
b. tan-V3
C. tan
Find the exact value of each real number y if it exists. Do NOT use a calculator.
1. y = arccos(-
2. y = arcsin(-V2)
3. y = arcsec(
QUESTION 4
Solve the problem.
On a Touch-Tone phone, each button produces a unique sound. The sound produced is the sum of two tones, given by
y = sin (2mlt) and y = sin (2Tht)
y%3D
where I and h are the low and high frequencies (cycles per second) shown on the illustration.
Touch-Tone phone
%3D
697
cycles/sec
770
cycles/sec
852
cycles/sec
941
cycles/sec
466
8 9
1209 1336 1477
cycles cycles cycies
sec
sec
sec
The sound produced is thus given by
y sin (2mlt) + sin (2Tht)
Write the sound emitted by touching the 7 key as a product of sines and cosines.
O y= 2 sin(2061nt) cos(357t)
Oy=2 sin(484Tt) cos(2188T))
Oy 2 sin(357TTT) cos(2061 t)
Oy 2 sin(2188TTT) cos(484Trt)
QUESTION 5
Express the sum or difference as a product of sines and/or cosines.
50
Chapter 8 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Ch. 8.1 - Find the degree measure of 1 rad.Ch. 8.1 - Without using a calculator, find: (A)cot 45 (B)cos...Ch. 8.1 - Solve the right triangle in Figure 14. Round side...Ch. 8.1 - Solve the right triangle in Figure 16. Round...Ch. 8.1 - Repeat Example 5 assuming that the man is standing...Ch. 8.1 - Prob. 1EDCh. 8.1 - Prob. 1ECh. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...
Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10ECh. 8.1 - In Problems 916, find the trigonometric ratio by...Ch. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - In Problems 916, find the trigonometric ratio by...Ch. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - In Problems 1724, find the exact value without...Ch. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - In Problems 1724, find the exact value without...Ch. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - In Problems 2536, use a calculator set in degree...Ch. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - In Problems 2536, use a calculator set in degree...Ch. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - In Problems 2536, use a calculator set in degree...Ch. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - In Problems 3742, use a calculator to find the...Ch. 8.1 - Prob. 40ECh. 8.1 - In Problems 3742, use a calculator to find the...Ch. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Digital display. An 8-foot-tall digital display...Ch. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - An angle above the horizontal is called an angle...Ch. 8.1 - An angle above the horizontal is called an angle...Ch. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.2 - Referring to Figure 2, find (A) sin 180(B)...Ch. 8.2 - Find the exact values without using a calculator....Ch. 8.2 - Find the exact values without using a calculator....Ch. 8.2 - Refer to Example 4. (A)Find the exact value of...Ch. 8.2 - Prob. 1EDCh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - In Problems 18, find the exact value of each...Ch. 8.2 - Prob. 4ECh. 8.2 - In Problems 18, find the exact value of each...Ch. 8.2 - Prob. 6ECh. 8.2 - In Problems 18, find the exact value of each...Ch. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - Prob. 30ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - Prob. 33ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - Prob. 39ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - Prob. 48ECh. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - Prob. 50ECh. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - Find the domain of the tangent function.Ch. 8.2 - Find the domain of the cotangent function.Ch. 8.2 - Find the domain of the secant function.Ch. 8.2 - Prob. 62ECh. 8.2 - Explain why the range of the cosecant function is...Ch. 8.2 - Explain why the range of the secant function is...Ch. 8.2 - Explain why the range of the cotangent function is...Ch. 8.2 - Explain why the range of the tangent function is...Ch. 8.2 - Seasonal business cycle. Suppose that profits on...Ch. 8.2 - Seasonal business cycle. Revenues from sales of a...Ch. 8.2 - Prob. 69ECh. 8.2 - Pollution. In a large city, the amount of sulfur...Ch. 8.2 - Prob. 71ECh. 8.3 - Find each of the following derivatives:...Ch. 8.3 - Find the slope of the graph of f(x) = cos x at...Ch. 8.3 - Find ddxcscx.Ch. 8.3 - Suppose that revenues from the sale of ski jackets...Ch. 8.3 - Prob. 1EDCh. 8.3 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Prob. 22ECh. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Prob. 26ECh. 8.3 - Find the slope of the graph of f(x) = sin x at x =...Ch. 8.3 - Find the slope of the graph of f(x) = cos x at x =...Ch. 8.3 - Prob. 29ECh. 8.3 - From the graph of y = f'(x) on the next page,...Ch. 8.3 - Prob. 31ECh. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - In Problems 39 and 40, find f(x). 39.f(x) = ex sin...Ch. 8.3 - Prob. 40ECh. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - Prob. 43ECh. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - Profit. Suppose that profits on the sale of...Ch. 8.3 - Revenue. Revenues from sales of a soft drink over...Ch. 8.3 - Physiology. A normal seated adult inhales and...Ch. 8.3 - Pollution. In a large city, the amount of sulfur...Ch. 8.4 - Find the area under the cosine curve y = cos x...Ch. 8.4 - Find cos20tdt.Ch. 8.4 - Find sinxcosxdx.Ch. 8.4 - Prob. 4MPCh. 8.4 - Suppose that revenues from the sale of ski jackets...Ch. 8.4 - Prob. 1ECh. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - Prob. 8ECh. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Prob. 13ECh. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Prob. 18ECh. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Find the shaded area under the cosine curve in the...Ch. 8.4 - Find the shaded area under the sine curve in the...Ch. 8.4 - Use a calculator to evaluate the definite...Ch. 8.4 - Prob. 26ECh. 8.4 - Use a calculator to evaluate the definite...Ch. 8.4 - Prob. 28ECh. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Given the definite integral I=03exsinxdx (A)Graph...Ch. 8.4 - Given the definite integral I=03excosxdx (A)Graph...Ch. 8.4 - Seasonal business cycle. Suppose that profits on...Ch. 8.4 - Seasonal business cycle. Revenues from sales of a...Ch. 8.4 - Pollution. In a large city, the amount of sulfur...Ch. 8 - Convert to radian measure in terms of : (A) 30(B)...Ch. 8 - Evaluate without using a calculator: (A) cos (B)...Ch. 8 - In Problems 36, find each derivative or integral....Ch. 8 - In Problems 36, find each derivative or integral....Ch. 8 - Prob. 5RECh. 8 - In Problems 36, find each derivative or integral....Ch. 8 - Convert to degree measure: (A) /6(B) /4(C) /3(D)...Ch. 8 - Evaluate without using a calculator: (A) sin6(B)...Ch. 8 - Evaluate with the use of a calculator: (A) cos...Ch. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - In Problems 1218, find each derivative or...Ch. 8 - In Problems 1218, find each derivative or...Ch. 8 - In Problems 1218, find each derivative or...Ch. 8 - Prob. 15RECh. 8 - In Problems 1218, find each derivative or...Ch. 8 - Prob. 17RECh. 8 - In Problems 1218, find each derivative or...Ch. 8 - Prob. 19RECh. 8 - Find the area under the sine curve y = sin x from...Ch. 8 - Given the definite integral I=15sinxxdx (A)Graph...Ch. 8 - Convert 15 to radian measure.Ch. 8 - Evaluate without using a calculator: (A) sin32 (B)...Ch. 8 - Prob. 24RECh. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2931, graph each function on a...Ch. 8 - In Problems 2931, graph each function on a...Ch. 8 - In Problems 2931, graph each function on a...Ch. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RE
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