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
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 8.1, Problem 36E
To determine
To find: The value of the expression
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
not use ai please
A graph of the function f is given below:
Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1
Of is defined at a.
If is not defined at x = a.
Of is continuous at x = a.
If is discontinuous at x = a.
Of is smooth at x = a.
Of is not smooth at = a.
If has a horizontal tangent line at = a.
f has a vertical tangent line at x = a.
Of has a oblique/slanted tangent line at x = a.
If has no tangent line at x = a.
f(a + h) - f(a)
lim
is finite.
h→0
h
f(a + h) - f(a)
lim
h->0+
and lim
h
h->0-
f(a + h) - f(a)
h
are infinite.
lim
does not exist.
h→0
f(a+h) - f(a)
h
f'(a) is defined.
f'(a) is undefined.
If is differentiable at x = a.
If is not differentiable at x = a.
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).…
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 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.arrow_forwardFind 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≤20arrow_forward[3] Use a substitution to rewrite sn(x) as 8n(x) = 1 2π C sin 2n+1 sin f(x+u)du.arrow_forward
- Differentiate the following functions. (a) y(x) = x³+6x² -3x+1 (b) f(x)=5x-3x (c) h(x) = sin(2x2)arrow_forwardx-4 For the function f(x): find f'(x), the third derivative of f, and f(4) (x), the fourth derivative of f. x+7arrow_forwardIn x For the function f(x) = find f'(x). Then find f''(0) and f''(9). 11x'arrow_forward
- Let f(x) = √√x+3 and g(x) = 6x − 2. Find each of the following composite functions and state the domain: (a) fog (b) gof, (c) fof (d) gogarrow_forwardCompute the following: (a) 8x³ + 3x dx (b) cos(2u) du (c) f² ebx dxarrow_forwardFind the following limits. (a) lim 3(x-1)² x→2 x (b) lim 0+x (c) lim 3x2-x+1 x²+3 x²+x-12 x-3 x-3arrow_forward
- For f(x) = (x+3)² - 2 sketch f(x), f(x), f(x − 2), and f(x) — 2. State the coordi- nates of the turning point in each graph.arrow_forwardif the b coloumn of a z table disappeared what would be used to determine b column probabilitiesarrow_forwardConstruct a model of population flow between metropolitan and nonmetropolitan areas of a given country, given that their respective populations in 2015 were 263 million and 45 million. The probabilities are given by the following matrix. (from) (to) metro nonmetro 0.99 0.02 metro 0.01 0.98 nonmetro Predict the population distributions of metropolitan and nonmetropolitan areas for the years 2016 through 2020 (in millions, to four decimal places). (Let x, through x5 represent the years 2016 through 2020, respectively.) x₁ = x2 X3 261.27 46.73 11 259.59 48.41 11 257.96 50.04 11 256.39 51.61 11 tarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities; Author: Mathispower4u;https://www.youtube.com/watch?v=OmJ5fxyXrfg;License: Standard YouTube License, CC-BY