Mathematical Applications for the Management, Life, and Social Sciences
11th Edition
ISBN: 9781305108042
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Chapter 14.2, Problem 12E
To determine
To calculate: The partial derivatives
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Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b).
x-a
f(x)=
1 - cos (4x-4)
3(x-1)²
; a = 1
a. Use a graphing utility to graph f. Select the correct graph below..
A.
W
→
✓
Each graph is displayed in a [- 1,3] by [0,5] window.
B.
in
✓
○ C.
und
☑
Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
x-1
○ A. The limit appears to be approximately ☐ .
(Round to the nearest tenth as needed.)
B. The limit does not exist.
b. Evaluate f(x) for values of x near 1 to support your conjecture.
X
0.9
0.99
0.999
1.001
1.01
1.1
f(x)
○ D.
+
☑
(Round to six decimal places as needed.)
Does the table from the previous step support your conjecture?
A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…
x²-19x+90
Let f(x) =
.
Complete parts (a) through (c) below.
x-a
a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
x→a+
○ A.
a=
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There are no values of a for which the limit equals a finite number.
b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
x→a+
A.
(Type integers or simplified fractions)
C. There are no values of a that satisfy lim f(x) = ∞.
+
x-a
c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
x→a+
A. Either a
(Type integers or simplified fractions)
B.
Sketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the following conditions.
f(2)=0
f(4) is undefined
lim f(x)=1
X-6
lim f(x) = -∞
x-0+
lim f(x) = ∞
lim f(x) = ∞
x-4
_8
Chapter 14 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
Ch. 14.1 - CHECKPOINT
1. Find the domain of the function
Ch. 14.1 - Prob. 1ECh. 14.1 - Prob. 2ECh. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9E
Ch. 14.1 - Prob. 10ECh. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.1 - Prob. 16ECh. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - Prob. 18ECh. 14.1 - Prob. 19ECh. 14.1 - Prob. 20ECh. 14.1 - Prob. 21ECh. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - Prob. 23ECh. 14.1 - Prob. 24ECh. 14.1 - Prob. 25ECh. 14.1 - Temperature-humidity models There are different...Ch. 14.1 - Prob. 28ECh. 14.1 - 29. Mortgage The following tables show that a...Ch. 14.1 - 30. Wind chill Wind and cold temperatures combine...Ch. 14.1 - Prob. 31ECh. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.1 - Prob. 34ECh. 14.1 - Prob. 35ECh. 14.1 - 36. Profit The Kirk Kelly Kandy Company makes two...Ch. 14.1 - Prob. 37ECh. 14.1 - Prob. 38ECh. 14.2 - Prob. 1CPCh. 14.2 - Prob. 2CPCh. 14.2 - Prob. 3CPCh. 14.2 - Prob. 4CPCh. 14.2 - Prob. 5CPCh. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Prob. 12ECh. 14.2 - Prob. 13ECh. 14.2 - Prob. 14ECh. 14.2 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 -
19. Find the slope of the tangent in the...Ch. 14.2 -
20. Find the slope of the tangent in the...Ch. 14.2 - Prob. 21ECh. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - Prob. 27ECh. 14.2 - Prob. 28ECh. 14.2 - Prob. 29ECh. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - 32. If , find the following.
(a) (b) (c) (d)
Ch. 14.2 - 33. If , find the following.
Ch. 14.2 - 34. If , find the following.
Ch. 14.2 - Prob. 35ECh. 14.2 -
Ch. 14.2 -
Ch. 14.2 - Prob. 38ECh. 14.2 - Prob. 39ECh. 14.2 - Prob. 40ECh. 14.2 - 41. .
Ch. 14.2 - .
Ch. 14.2 - Prob. 43ECh. 14.2 -
Ch. 14.2 - 45. Mortgage When a homeowner has a 25-year...Ch. 14.2 - 46. Mass transportation ridership Suppose that in...Ch. 14.2 - 47. Wilson's lot size formula In economics, the...Ch. 14.2 - 48. Cost Suppose that the total cost (in dollars)...Ch. 14.2 - 49. Pesticide Suppose that the number of thousands...Ch. 14.2 - 50. Profit Suppose that the profit (in dollars)...Ch. 14.2 - Prob. 51ECh. 14.2 - Prob. 52ECh. 14.2 - 53. Production Suppose that the output Q (in...Ch. 14.2 - Prob. 54ECh. 14.2 - Prob. 55ECh. 14.2 - Prob. 56ECh. 14.3 - CHECKPOINT
If the joint cost in dollars for two...Ch. 14.3 - Prob. 2CPCh. 14.3 - Prob. 3CPCh. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - 3. The total cost of producing 1 unit of a product...Ch. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14.3 - 9. If the joint cost function for two products is
...Ch. 14.3 - 10. Suppose the joint cost function for x units of...Ch. 14.3 - 11. Suppose that the joint cost function for two...Ch. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Prob. 14ECh. 14.3 - Prob. 15ECh. 14.3 - Prob. 16ECh. 14.3 - Prob. 17ECh. 14.3 - Prob. 18ECh. 14.3 - Prob. 19ECh. 14.3 - Prob. 20ECh. 14.3 - 21. Suppose the Cobb-Douglas production function...Ch. 14.3 - Prob. 22ECh. 14.3 - Prob. 23ECh. 14.3 - Prob. 24ECh. 14.3 - Prob. 25ECh. 14.3 - Prob. 26ECh. 14.3 - Prob. 27ECh. 14.3 - Prob. 28ECh. 14.3 - Prob. 29ECh. 14.3 - Prob. 30ECh. 14.4 - CHECKPOINT
Suppose that
Find
Ch. 14.4 - Prob. 2CPCh. 14.4 - Prob. 3CPCh. 14.4 - Prob. 4CPCh. 14.4 - Prob. 1ECh. 14.4 - Prob. 2ECh. 14.4 - Prob. 3ECh. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - Prob. 6ECh. 14.4 - Prob. 7ECh. 14.4 - Prob. 8ECh. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - 19. Profit Suppose that the quarterly profit from...Ch. 14.4 - Prob. 20ECh. 14.4 - 21. Nutrition A new food is designed to add weight...Ch. 14.4 - Prob. 22ECh. 14.4 - 23. Production Suppose that
tons
is the...Ch. 14.4 - 24. Production Suppose that x units of one input...Ch. 14.4 - 25. Profit Suppose that a manufacturer produces...Ch. 14.4 - Prob. 26ECh. 14.4 - Prob. 27ECh. 14.4 - Prob. 28ECh. 14.4 - 29. Profit A company manufactures two products, A...Ch. 14.4 - Prob. 30ECh. 14.4 - Prob. 31ECh. 14.4 - The manager of the Sea Islands Chicken Shack is...Ch. 14.4 - Prob. 34ECh. 14.4 - Prob. 35ECh. 14.4 - Prob. 36ECh. 14.5 - Prob. 1CPCh. 14.5 - Prob. 2CPCh. 14.5 - Prob. 3CPCh. 14.5 - Prob. 4CPCh. 14.5 - Prob. 1ECh. 14.5 - Prob. 2ECh. 14.5 - Prob. 3ECh. 14.5 - Prob. 4ECh. 14.5 - Prob. 5ECh. 14.5 - Prob. 6ECh. 14.5 - Prob. 7ECh. 14.5 - Prob. 8ECh. 14.5 - Prob. 9ECh. 14.5 - Prob. 10ECh. 14.5 - Prob. 11ECh. 14.5 - Prob. 12ECh. 14.5 - Prob. 13ECh. 14.5 - Prob. 14ECh. 14.5 - Prob. 15ECh. 14.5 - 16. Utility Suppose that the budget constraint in...Ch. 14.5 - 17. Utility Suppose that the utility function for...Ch. 14.5 - 18. Utility Suppose that the utility function for...Ch. 14.5 - Prob. 19ECh. 14.5 - Prob. 20ECh. 14.5 - 21. Cost A firm has two plants, X and Y. Suppose...Ch. 14.5 - Prob. 22ECh. 14.5 - Prob. 23ECh. 14.5 - Prob. 24ECh. 14.5 - 25. Manufacturing Find the dimensions (in...Ch. 14.5 - Prob. 26ECh. 14 - 1. What is the domain of ?
Ch. 14 - Prob. 2RECh. 14 - Prob. 3RECh. 14 - 4. If .
Ch. 14 - Prob. 5RECh. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - Prob. 14RECh. 14 - In Problems 15-18, find the second partials.
Ch. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RECh. 14 - Prob. 22RECh. 14 - Prob. 23RECh. 14 - Prob. 24RECh. 14 - Prob. 25RECh. 14 - Prob. 26RECh. 14 - Prob. 27RECh. 14 - Prob. 28RECh. 14 - Prob. 29RECh. 14 - Prob. 30RECh. 14 - Prob. 31RECh. 14 - Prob. 32RECh. 14 - Prob. 33RECh. 14 - Prob. 34RECh. 14 - 35. Modeling US. average wage The table gives the...Ch. 14 - Prob. 36RECh. 14 - Prob. 1TCh. 14 - Prob. 2TCh. 14 - Prob. 3TCh. 14 - Prob. 4TCh. 14 - Prob. 5TCh. 14 - Prob. 6TCh. 14 - 7. Suppose the demand functions for two products...Ch. 14 - Prob. 8TCh. 14 - 9. Find x and y that maximize the utility function...Ch. 14 - Prob. 10T
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