Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
13th Edition
ISBN: 9780321869838
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
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Textbook Question
Chapter 8.1, Problem 41E
In Problems 27-42, find the exact value of each expression without using a calculator.
41. cot (– 45°)
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The graph below is the function f(z)
4
3
-2
-1
-1
1
2
3
-3
Consider the function f whose graph is given above.
(A) Find the following. If a function value is undefined, enter "undefined". If a limit does not exist, enter
"DNE". If a limit can be represented by -∞o or ∞o, then do so.
lim f(z)
+3
lim f(z)
1-1
lim f(z)
f(1)
= 2
=
-4
= undefined
lim f(z) 1
2-1
lim f(z):
2-1+
lim f(x)
2+1
-00
= -2
= DNE
f(-1) = -2
lim f(z) = -2
1-4
lim f(z)
2-4°
00
f'(0)
f'(2)
=
=
(B) List the value(s) of x for which f(x) is discontinuous. Then list the value(s) of x for which f(x) is left-
continuous or right-continuous. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5). If
there are none, enter "none".
Discontinuous at z =
Left-continuous at x =
Invalid use of a comma.syntax incomplete.
Right-continuous at z =
Invalid use of a comma.syntax incomplete.
(C) List the value(s) of x for which f(x) is non-differentiable. Enter your answer as a comma-separated list,
if needed (eg. -2, 3, 5).…
A graph of the function f is given below:
Study the graph of f at the value given below. Select each of the following that applies for the value
a = -4.
f is defined at = a.
f is not defined at 2 = a.
If is continuous at x = a.
Of is discontinuous at x = a.
Of is smooth at x = a.
f is not smooth at x = a.
If has a horizontal tangent line at x = a.
f has a vertical tangent line at x = a.
Of has a oblique/slanted tangent line at x = a.
Of has no tangent line at x = a.
f(a + h) − f(a)
h
lim
is finite.
h→0
f(a + h) - f(a)
lim
is infinite.
h→0
h
f(a + h) - f(a)
lim
does not exist.
h→0
h
f'(a) is defined.
f'(a) is undefined.
If is differentiable at x = a.
If is not differentiable at x = a.
Find the point of diminishing returns (x,y) for the function R(X), where R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in
thousands of dollars).
R(x) = 10,000-x3 + 42x² + 700x, 0≤x≤20
Chapter 8 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Ch. 8.1 - Find the degree measure of 1 rad.Ch. 8.1 - Prob. 2MPCh. 8.1 - Prob. 3MPCh. 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 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - Prob. 30ECh. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - Prob. 33ECh. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - Prob. 39ECh. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - In Problems 27-42, find the exact value of each...Ch. 8.1 - In Problems 4354, use a calculator in radian or...Ch. 8.1 - In Problems 4354, use a calculator in radian or...Ch. 8.1 - In Problems 4354, use a calculator in radian or...Ch. 8.1 - In Problems 4354, use a calculator in radian or...Ch. 8.1 - In Problems 4354, use a calculator in radian or...Ch. 8.1 - Prob. 48ECh. 8.1 - In Problems 4354, use a calculator in radian or...Ch. 8.1 - Prob. 50ECh. 8.1 - In Problems 4354, use a calculator in radian or...Ch. 8.1 - In Problems 4354, use a calculator in radian or...Ch. 8.1 - In Problems 4354, use a calculator in radian or...Ch. 8.1 - In Problems 4354, use a calculator in radian or...Ch. 8.1 - In Problems 5558, use a graphing calculator set in...Ch. 8.1 - In Problems 5558, use a graphing calculator set in...Ch. 8.1 - In Problems 5558, use a graphing calculator set in...Ch. 8.1 - In Problems 5558, use a graphing calculator set in...Ch. 8.1 - Find the domain of the tangent function.Ch. 8.1 - Find the domain of the cotangent function.Ch. 8.1 - Find the domain of the secant function.Ch. 8.1 - Prob. 62ECh. 8.1 - Explain why the range of the cosecant function is...Ch. 8.1 - Explain why the range of the secant function is...Ch. 8.1 - Explain why the range of the cotangent function is...Ch. 8.1 - Explain why the range of the tangent function is...Ch. 8.1 - Seasonal business cycle. Suppose that profits on...Ch. 8.1 - Seasonal business cycle. Revenues from sales of a...Ch. 8.1 - Prob. 69ECh. 8.1 - Pollution. In a large city, the amount of sulfur...Ch. 8.1 - Prob. 71ECh. 8.2 - Find each of the following derivatives:...Ch. 8.2 - Find the slope of the graph of f(x) = cos x at...Ch. 8.2 - Find ddxcscx.Ch. 8.2 - Suppose that revenues from the sale of ski jackets...Ch. 8.2 - Prob. 1EDCh. 8.2 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.2 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.2 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.2 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.2 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Prob. 22ECh. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Find the indicated derivatives in Problems 926....Ch. 8.2 - Prob. 26ECh. 8.2 - Find the slope of the graph of f(x) = sin x at x =...Ch. 8.2 - Find the slope of the graph of f(x) = cos x at x =...Ch. 8.2 - Prob. 29ECh. 8.2 - From the graph of y = f'(x) on the next page,...Ch. 8.2 - Prob. 31ECh. 8.2 - Find the indicated derivatives in Problems 3138....Ch. 8.2 - Find the indicated derivatives in Problems 3138....Ch. 8.2 - Find the indicated derivatives in Problems 3138....Ch. 8.2 - Find the indicated derivatives in Problems 3138....Ch. 8.2 - Find the indicated derivatives in Problems 3138....Ch. 8.2 - Find the indicated derivatives in Problems 3138....Ch. 8.2 - Find the indicated derivatives in Problems 3138....Ch. 8.2 - In Problems 39 and 40, find f(x). 39.f(x) = ex sin...Ch. 8.2 - Prob. 40ECh. 8.2 - In Problems 4146, graph each function on a...Ch. 8.2 - In Problems 4146, graph each function on a...Ch. 8.2 - Prob. 43ECh. 8.2 - In Problems 4146, graph each function on a...Ch. 8.2 - In Problems 4146, graph each function on a...Ch. 8.2 - In Problems 4146, graph each function on a...Ch. 8.2 - Profit. Suppose that profits on the sale of...Ch. 8.2 - Revenue. Revenues from sales of a soft drink over...Ch. 8.2 - Physiology. A normal seated adult inhales and...Ch. 8.2 - Pollution. In a large city, the amount of sulfur...Ch. 8.3 - Find the area under the cosine curve y = cos x...Ch. 8.3 - Find cos20tdt.Ch. 8.3 - Find sinxcosxdx.Ch. 8.3 - Prob. 4MPCh. 8.3 - Suppose that revenues from the sale of ski jackets...Ch. 8.3 - Prob. 1ECh. 8.3 - In Problems 18, by using only the unit circle...Ch. 8.3 - In Problems 18, by using only the unit circle...Ch. 8.3 - In Problems 18, by using only the unit circle...Ch. 8.3 - In Problems 18, by using only the unit circle...Ch. 8.3 - In Problems 18, by using only the unit circle...Ch. 8.3 - In Problems 18, by using only the unit circle...Ch. 8.3 - Prob. 8ECh. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Prob. 13ECh. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Prob. 18ECh. 8.3 - Evaluate each of the definite integrals in...Ch. 8.3 - Evaluate each of the definite integrals in...Ch. 8.3 - Evaluate each of the definite integrals in...Ch. 8.3 - Evaluate each of the definite integrals in...Ch. 8.3 - Find the shaded area under the cosine curve in the...Ch. 8.3 - Find the shaded area under the sine curve in the...Ch. 8.3 - Use a calculator to evaluate the definite...Ch. 8.3 - Prob. 26ECh. 8.3 - Use a calculator to evaluate the definite...Ch. 8.3 - Prob. 28ECh. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Find each of the indefinite integrals in Problems...Ch. 8.3 - Given the definite integral I=03exsinxdx (A)Graph...Ch. 8.3 - Given the definite integral I=03excosxdx (A)Graph...Ch. 8.3 - Seasonal business cycle. Suppose that profits on...Ch. 8.3 - Seasonal business cycle. Revenues from sales of a...Ch. 8.3 - 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 - 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. 13RECh. 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 - 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. 22RECh. 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. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RE
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