Technical Calculus
Solved Exam Questions
Course Introduction
Technical Calculus is designed to provide students with a solid foundation in calculus concepts and techniques used in technical and applied fields. The course covers fundamental topics such as limits, derivatives, and integrals, with a focus on practical applications to engineering technology, physical sciences, and computer science. Students will develop problem-solving skills by analyzing real-world scenarios involving rates of change, optimization, and area under curves, using both analytical and numerical methods. Emphasis is placed on interpreting calculus results in the context of technical applications, ensuring that graduates are prepared to apply these mathematical tools effectively in their chosen careers.
Recommended Textbook
Calculus An Applied Approach 10th Edition by Ron Larson
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11 Chapters
1279 Verified Questions
1279 Flashcards
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Chapter 1: Functions, graphs, and Limits
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427 Verified Questions
427 Flashcards
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Sample Questions
Q1) A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place.
A) -24.1 feet/second
B) -0.2 feet/second
C) -0.6 feet/second
D) -15 feet/second
E) -0.9 feet/second
Answer: D
Q2) What lump sum should be deposited in an account that will earn at an annual rate of 9%,compounded quarterly,to grow to $150,000 for retirement in 20 years? Round your answer to the nearest cent.
A) $147,330.10
B) $18,292.68
C) $53,571.43
D) $24,961.93
E) $25,294.49
Answer: E
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Chapter 2: Differentiation
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Sample Questions
Q1) The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long?
A) 96 ft<sup>2</sup>/min
B) 1,008 ft<sup>2</sup>/min
C) 504 ft<sup>2</sup>/min
D) 2,016 ft<sup>2</sup>/min
E) 84 ft<sup>2</sup>/min
Answer: B
Q2) A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place.
A) -24.1 feet/second
B) -0.2 feet/second
C) -0.6 feet/second
D) -15 feet/second
E) -0.9 feet/second
Answer: D
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Chapter 3: Applications of the Derivative
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Sample Questions
Q1) Find the length and width of a rectangle that has perimeter 56 meters and a maximum area.
A) 7, 21
B) 1, 27
C) 14, 14
D) 15, 13
E) 18,10
Answer: C
Q2) A travel agency will plan a tour for groups of size 53 or larger.If the group contains exactly 53 people,the price is $800 per person.However,each person's price is reduced by $10 for each additional person above the 53.If the travel agency incurs a price of $150 per person for the tour,what size group will give the agency the maximum profit?
A) 6
B) 91
C) 59
D) 70
E) 32
Answer: C
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Chapter 4: Exponential and Logarithmic Functions
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Sample Questions
Q1) How much more interest will be earned if $7,000 is invested for 9 years at an annual rate of 9% compounded continuously,instead of at 9% compounded quarterly? Round your answer to the nearest cent.
A) $47.49
B) $93.15
C) $140.64
D) $2,924.71
E) $3,017.87
Q2) To help their son buy a car on his 16th birthday,a boy's parents invest $1,900 on his 10th birthday.If the investment pays an annual rate of 9% compounded continuously,how much is available on his 16th birthday? Round your answer to the nearest cent.
A) $3,240.96
B) $3,260.41
C) $3,186.49
D) $2,926.00
E) $16,475.16
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Chapter 5: Integration and Its Applications
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88 Flashcards
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Sample Questions
Q1) A ball is thrown vertically upwards from a height of 6 ft with an initial velocity of 40 ft per second.
How high will the ball go?
A) 29.03 ft
B) 29.34 ft
C) 30.89 ft
D) 25.02 ft
E) 32.12 ft
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Chapter 6: Techniques of Integration
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Sample Questions
Q1) Suppose the mean height of American women between the ages of 30 and 39 is 64.5 inches,and the standard deviation is 2.7 inches.Use a symbolic integration utility to approximate the probability that a 30-to 39-year-old woman chosen at random is between 5 feet 4 inches and 6 feet tall.
A) 0.5734
B) 0.5707
C) 0.8547
D) 0.9522
E) 0.4257
Q2) A business is expected to yield a continuous flow of profit at the rate of $200,000 per year.If money will earn interest at the nominal rate of 2% per year compounded continuously,what is the present value of the business forever?
A) $10,100,000
B) $1,000,000
C) $10,000,000
D) $10,010,000
E) $1,100,000
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Chapter 7: Functions of Several Variables
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113 Flashcards
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Sample Questions
Q1) Determine whether the statement is true or false.If it is false,explain why or give an example that shows it is false.
A linear regression model with a positive correlation will have a slope that is greater than 0.
A)True
B)False
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Chapter 8: Trigonometric Functions
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Sample Questions
Q1) A compact disc can have an angular speed up to 3,154 radians per minute.At this angular speed,how many revolutions per minute would the CD make? Round your answer to the nearest integer.
A) 1,004
B) 1,577
C) 402
D) 502
E) 251
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Chapter 9: Probability and Calculus
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36 Flashcards
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Sample Questions
Q1) Three people are asked their opinions on a political issue.They can answer Opposed (O)or Undecided (U).Find the sample space S.
A) {OOO, OOU, OUO, UOO, UUU, UUO, UOU}
B) {OOO, OOU, UOO, UUU, UUO, UOU, OUU}
C) {OOO, OOU, OUO, UOO, UUO, UOU, OUU}
D) {OOO, OUO, UOO, UUO, UOU, OUU}
E) {OOO,OOU,OUO,UOO,UUU,UUO,UOU,OUU}
Q2) A coin is tossed three times.Describe the event A that at least two tails occur.
A) {TTT, THH, THT, HHT}
B) {HHH, TTH, THT, HTT}
C) {TTT, TTH, THT, HTT}
D) {TTTT, TTHT, THTT, HTTT}
E) {TT,HT,TH}
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Chapter 10: Series and Taylor Polynomials
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Sample Questions
Q1) A factory is polluting a river such that at every mile down river from the factory an environmental expert finds 15% less pollutant than at the preceding mile.If the pollutant's concentration is 600 ppm (parts per million)at the factory,what is its concentration 12 miles down river?
A) 180 ppm
B) 90 ppm
C) 85.35 ppm
D) 705.88 ppm
E) 100.41 ppm
Q2) What are the next three terms in the arithmetic sequence -2,-6,-10,....
A) -14, -18, -22
B) 2, 6, 10
C) 56, -224, 896
D) -8, -10, -12
E) -10,-14,-18
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Chapter 11: Differential Equations
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Sample Questions
Q1) A population of eight beavers has been introduced into a new wetlands area.Biologists estimate that the maximum population the wetlands can sustain is 60 beavers.After 3 years,the population is 15 beavers.The population follows a Gompertz growth model.How many beavers will there be in the wetlands after 10 years?
A) 34 beavers
B) 32 beavers
C) 30 beavers
D) 31 beavers
E) 39 beavers
Q2) The rate of change of the population of a city is proportional to the population P at any time (in years).In 2000,the population was 200,000,and the constant of proportionality was 0.015.Estimate the population of the city in the year 2020.
A) 260,972 people
B) 268,972 people
C) 263,972 people
D) 266,972 people
E) 269,972 people
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