CALCULUS+ITS APPLICATIONS-MYMATHLAB
15th Edition
ISBN: 9780137590438
Author: Goldstein
Publisher: PEARSON
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Textbook Question
Chapter 5.2, Problem 3E
Savings Account Four thousand dollars is deposited in a savings account at
a. What is the formula for
b. What
c. How much money will be in the account after
d. When will the balance reach
e. How fast is the balance growing when it reaches
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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 5 Solutions
CALCULUS+ITS APPLICATIONS-MYMATHLAB
Ch. 5.1 - a. Solve the differential equation...Ch. 5.1 - Under ideal conditions a colony of Escherichia...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...
Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - Population and Exponential Growth Let P(t) be the...Ch. 5.1 - Growth of a Colony of Fruit Flies A colony of...Ch. 5.1 - GrowthConstant for a Bacteria Culture Abacteria...Ch. 5.1 - Growth of a Bacteria Culture The initial size of a...Ch. 5.1 - Using the Differential Equation Let P(t) be the...Ch. 5.1 - Growth of Bacteria Approximately 10,000 bacteria...Ch. 5.1 - Growth of cells After t hours, there are P(t)...Ch. 5.1 - Insect Population The size of a certain insect...Ch. 5.1 - Population Growth Determine the growth constant of...Ch. 5.1 - Time to Triple Determine the growth constant of a...Ch. 5.1 - Exponential Growth A population is growing...Ch. 5.1 - Time to DoubleA population is growing...Ch. 5.1 - Exponential Growth The rate of growth of a certain...Ch. 5.1 - Worlds Population The worlds population was 5.51...Ch. 5.1 - Prob. 33ECh. 5.1 - A Population Model The population (in millions) of...Ch. 5.1 - Radioactive Decay A sample of 8 grams of...Ch. 5.1 - Radioactive Decay Radium 226 is used in cancer...Ch. 5.1 - Decay of Penicillin in the Bloodstream A person is...Ch. 5.1 - Radioactive Decay Ten grams of a radioactive...Ch. 5.1 - Radioactive Decay The decay constant for the...Ch. 5.1 - Drug ConstantRadioactive cobalt 60 has a half-life...Ch. 5.1 - Iodine Level in Dairy Products If dairy cows eat...Ch. 5.1 - Half-Life Ten grams of a radioactive material...Ch. 5.1 - Decay of Sulfate in the Bloodstream In an animal...Ch. 5.1 - Radioactive Decay Forty grams of a certain...Ch. 5.1 - Radioactive Decay A sample of radioactive material...Ch. 5.1 - Rate of Decay A sample of radioactive material has...Ch. 5.1 - Carbon Dating In 1947, a cave with beautiful...Ch. 5.1 - King Arthur's Round Table According to legend, in...Ch. 5.1 - Prob. 49ECh. 5.1 - Population of the PacificNorthwest In 1938,...Ch. 5.1 - Time of the Fourth Ice Age Many scientists believe...Ch. 5.1 - Time Constant Let T be the time constant of the...Ch. 5.1 - Prob. 53ECh. 5.1 - Time Constant and Half-life Consider as...Ch. 5.1 - An Initial Value Problem Suppose that the function...Ch. 5.1 - Time to Finish Consider the exponential decay...Ch. 5.2 - One thousand dollars is to be invested in a bank...Ch. 5.2 - A building was bought for 150,000 and sold 10...Ch. 5.2 - Savings Account Let A(t)=5000e0.04t be the balance...Ch. 5.2 - Savings Account Let A(t) be the balance in a...Ch. 5.2 - Savings Account Four thousand dollars is deposited...Ch. 5.2 - Savings Account Ten thousand dollars is deposited...Ch. 5.2 - Investment AnalysisAn investment earns 4.2 yearly...Ch. 5.2 - Investment Analysis An investment earns 5.1 yearly...Ch. 5.2 - Continuous Compound One thousand dollars is...Ch. 5.2 - Continuous Compound Ten thousand dollars is...Ch. 5.2 - Technology Stock One hundred shares of a...Ch. 5.2 - Appreciation of Art Work Pablo Picassos Angel...Ch. 5.2 - Investment Analysis How many years are required...Ch. 5.2 - Doubling an Investment What yearly interest rate...Ch. 5.2 - Tripling an Investment If an investment triples in...Ch. 5.2 - Prob. 14ECh. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Real Estate Investment A farm purchased in 2000...Ch. 5.2 - Real Estate Investment A parcel of land bought in...Ch. 5.2 - Present Value Find the present value of 1000...Ch. 5.2 - Prob. 20ECh. 5.2 - Present Value How much money must you invest now...Ch. 5.2 - Present Value If the present value of 1000 to be...Ch. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Differential Equation and InterestA small amount...Ch. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.3 - The current toll for the use of a certain toll...Ch. 5.3 - The current toll for the use of a certain toll...Ch. 5.3 - The current toll for the use of a certain toll...Ch. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Prob. 2ECh. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Prob. 6ECh. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Prob. 8ECh. 5.3 - Percentage Rate of Growth The annual sales S(in...Ch. 5.3 - Prob. 10ECh. 5.3 - Price of Ground Beef The wholesale price in...Ch. 5.3 - Price of Pork The wholesale price in dollars of...Ch. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - Prob. 14ECh. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - Prob. 18ECh. 5.3 - Elasticity of Demand Currently 1800 people ride a...Ch. 5.3 - Prob. 20ECh. 5.3 - Elasticity of Demand A movie theater has a seating...Ch. 5.3 - Prob. 22ECh. 5.3 - Elasticity of Demand A country that is the major...Ch. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.4 - A sociological study was made to examine the...Ch. 5.4 - Prob. 2CYUCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5 - What differential equation is key to solving...Ch. 5 - Prob. 2FCCECh. 5 - Prob. 3FCCECh. 5 - Explain how radiocarbon dating works.Ch. 5 - Prob. 5FCCECh. 5 - Prob. 6FCCECh. 5 - Define the elasticity of demand, E(p), for a...Ch. 5 - Describe an application of the differential...Ch. 5 - Prob. 9FCCECh. 5 - Atmospheric Pressure The atmospheric pressure...Ch. 5 - Population Model The herring gull population in...Ch. 5 - Present Value Find the present value of 10,000...Ch. 5 - Compound Interest One thousand dollars is...Ch. 5 - Half-Life The half-life of the radioactive element...Ch. 5 - Carbon Dating A piece of charcoal found at...Ch. 5 - Population Model From January 1, 2010, to January...Ch. 5 - Compound Interest A stock portfolio increased in...Ch. 5 - Comparing Investments An investor initially...Ch. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 - Prob. 18RECh. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RE
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