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mathematics
calculus with applications

Questions and Answers of Calculus With Applications

The monthly residential consumption of natural gas in Pennsylvania for 2009 is found in the following table.a. Plot the data, letting t = 1 correspond to January, t = 2 to February, and so on. Is it
Find each integral.(cos x)–4/3 sin x dx
Find each integral.∫(sin x)3/2 cos x dx
Find each integral.∫x2 cot 8x3 dx
Find each integral.∫x tan 11x2 dx
Find each integral.∫cos8 x sin x dx
Find each integral.∫√cos x sin x dx
Find each integral.∫5x sec 2x2 tan 2x2 dx
Find each integral.∫x2 sin 4x3 dx
Find each integral.∫4 csc2 x dx
Find each integral.∫8sec2 x dx
Find each integral.∫sec2 5x dx
Find each integral.∫tan 7x dx
Find each integral.∫cos 5x dx
Find each integral.∫sin 2x dx
Find each function value.tan 1.2915
Find each function value.cos 0.5934
Find each function value.cos 72°
Find each function value.sin 47°
Convert the following radian measures to degrees.13π/15
Convert the following radian measures to degrees.13π/20
Convert the following degree measures to radians. Leave answers as multiples of π.405°
Determine whether each of the following statements is true or false, and explain why.cos(a + b) – cos a + cos b
Find the derivatives of the functions defined as follows.y = cos4 x
The monthly residential consumption of petroleum (in trillions of BTUs) in the United States for 2009 is found in the following table.a. Plot the data, letting t = 1 correspond to January, t = 2
Find each integral.∫10x2 sin x/2 dx
Find each integral.∫–6x2 cos 8x dx
Find each integral.∫–11x cos x dx
Find each integral.∫4x sin x dx
Find each integral.∫7x sin 5x dx
Find each integral.∫–6x cos 5x dx
Find each integral.∫ex csc ex cot ex dx
Find each integral.∫e–x tan e–x dx
Find each integral.∫ex sin ex dx
Find each integral.∫(cot (– 3/8 x) dx
Find each integral.∫tan 1/3 x dx
Find each integral.∫2x7 cos x8 dx
Find each integral. cos x V sin x dx
Find each integral.∫3√cos x (sin x) dx
Find each integral.∫sin4 x cos x dx
Find each integral.∫sin7 x cos x dx
Find each integral.– ∫2 csc2 8x dx
Find each integral.– ∫3 sec2 3x dx
Find each integral.∫sin 5x dx
Find the derivatives of the functions defined as follows.y = 3 cot5 x
Find the derivatives of the functions defined as follows.y = tan8 x
Find the derivatives of the functions defined as follows.y = –9 sin5 x
Find the derivatives of the functions defined as follows.y = –cos 2x + cos π/6
Find the derivatives of the functions defined as follows.y = 1/2 sin 8x
Jenny Crum stands on a cliff at the edge of a canyon. On the opposite side of the canyon is another cliff equal in height to the one she is on. (See the figure.) By dropping a rock and timing its
The amount of electricity (in trillion BTUs) consumed by U.S. residential customers in 2009 is given in the following table.a. Plot the data, letting t = 1 correspond to January, t = 2 to February,
Find all values of x between 0 and 2π that satisfy each of the following equations.sec x = √2
Find all values of x between 0 and 2π that satisfy each of the following equations.sec x = –2/√3
Find all values of x between 0 and 2π that satisfy each of the following equations.tan x = √3
Find all values of x between 0 and 2π that satisfy each of the following equations.tan x = –1
Find all values of x between 0 and 2π that satisfy each of the following equations.sin x = –1/2
Find all values of x between 0 and 2π that satisfy each of the following equations.cos x = 1/2
Convert the following degree measures to radians. Leave answers as multiples of π.150°
It is anticipated that a bank stock that Jeff Marsalis has invested $16,000 in will achieve an annual interest rate of 9%. Determine the doubling time for this investment using the doubling-time
Michael Dew has invested $14,000 in a certificate of deposit that has a 3.25% annual interest rate. Determine the doubling time for this investment using the doubling-time formula. How does this
Ross Craycraft wants to expand his pharmacy. To do this, he takes out a bank loan of $49,275 and agrees to repay it at 12.2% compounded monthly over 48 months. Find the amount of each payment
Diane Antaya borrows $20,000 from the bank to help her expand her business. She agrees to repay the money in equal payments at the end of each year for 9 years. Interest is at 8.9% compounded
J. Euclid deposits $1526.38 at the end of each 6-month period in an account paying 7.6% compounded semiannually. How much will be in the account after 5 years?
Cathy Schneider deposits $491 at the end of each quarter for 9 years. If the account pays 9.4% compounded quarterly, find the final amount in the account.
In 4 years, Jack McCanna must pay a pledge of $5000 to his church’s building fund. He wants to set up a sinking fund to accumulate that amount. What should each semiannual payment into the fund be
In the year 2010, the proportion of U.S. major league baseball players who were foreign born was 231 out of 833. Suppose we begin to randomly select major league players until we find one who is
Infant mortality is an example of a relatively rare event that can be described by the Poisson distribution, for which the probability of x occurrences is given bya. Verify that f describes a
It is anticipated that a bank stock that Katie Vales has invested $15,000 in will achieve an annual interest rate of 6%. Determine the doubling time for this investment using the doubling-time
Ray Mesing has invested $12,000 in a certificate of deposit that has a 4.75% annual interest rate. Determine the doubling time for this investment using the doubling-time formula. How does this
Use the fact thatto find a Taylor series for (1 + x) /(1 - x). 1 + x 1- x 1 1- x + X 1-x
When Barbara Essenmacher opened her law office, she bought $14,000 worth of law books and $7200 worth of office furniture. She paid $1200 down and agreed to amortize the balance with semiannual
Kristina Walters buys a new car costing $22,000. She agrees to make payments at the end of each month for 4 years. If she pays 9% interest, compounded monthly, what is the amount of each payment?
Jerry Higgins bought a rare stamp for his collection. He agreed to pay a lump sum of $4000 after 5 years. Until then, he pays 6% interest, compounded semiannually.a. Find the amount of each
Rebecca Nasman sells some land in Nevada. She will be paid a lump sum of $60,000 in 7 years. Until then, the buyer pays 8% interest, compounded quarterly.a. Find the amount of each quarterly interest
Megan Donnelly wants to buy a car that she estimates will cost $24,000 in 5 years. How much money must she deposit at the end of each quarter at 5% interest compounded quarterly in order to have
Steve Day wants $20,000 in 8 years.a. What amount should he deposit at the end of each quarter at 6% annual interest compounded quarterly to accumulate the $20,000?b. Find his quarterly deposit if
For 8 years, Tobi Casper deposits $100 at the end of each month into an annuity paying 6% annual interest compounded monthly.a. Find the total amount Tobi deposits into the account over the 8
Sara Swangard wants to deposit $12,000 at the end of each year for 9 years into an annuity.a. Sara’s local bank offers an account paying 5% interest compounded annually. Find the final amount she
According to the National Center for Health Statistics, life expectancy for a 70-year-old African American male is 12.3 years. Assuming that from age 70, the survival of African American males
According to the National Center for Health Statistics, the life expectancy for a 55-year-old African American female is 26.1 years. Assuming that from age 55, the survival of African American
What is a z-score? How is it used?
The length of a leaf on a tree is a random variable with probability density function defined bya. What is the expected leaf length?b. Find σ for this distribution.c. Find the probability that the
The number of U.S. users (in millions) on Facebook, a computer social network, in 2009 is given in the table below.a. Plot the data. What type of function appears to best match this data?b. Use the
The National Highway Traffic Safety Administration records the time of day of fatal crashes. The following table gives the time of day (in hours since midnight) and the frequency of fatal
The report also predicted that the U.S. Asian population would increase from 10.7 million in 2000 to 33.4 million in 2050. Repeat Exercise 49 using this data.Data from Exercises 49A recent report by
A recent report by the U.S. Census Bureau predicts that the U.S. Hispanic population will increase from 35.6 million in 2000 to 102.6 million in 2050. Assuming the unlimited growth model dy/dt = ky
If inflation grows continuously at a rate of 5% per year, how long will it take for $1 to lose half its value?
The marginal profit of a certain company is given bywhere x represents the amount of money (in thousands of dollars) that the company spends on advertising. Find the profit for each advertising
Repeat Exercise 8, trying other functions of t in place of f(t) such as t3. Find which functions give a recognizable answer, and verify that answer using Equation (1).Data from Exercises 8Repeat
Repeat Exercise 7, but in place of f(t) put a * e Λ (–p * t), the form of PL(t) used in Exercises 5. Verify that the solution is equivalent to the solution given in Exercise 6.Data from Exercises
At the website Wolfram|Alpha.com, you can enter “y´(t) = (f(t) – y) * k, y(0) = a" to solve the initial value problem in this Extended Application, where we have used y(t) to represent PL(t),
When you simplify the right-hand side of Equation (1) using your new expression for the integral, and then factor out and divide by PL(0)you’ll get the following nice expression for the ratio
Suppose that instead of assuming that all pollution inflow immediately ceases, we model Pi(t) by a decaying exponential of the form a · e–pt where p is a constant that tells us how fast the inflow
We claim that Equation (1) is a solution of the differential equationwhere t measures time from the present. The constant k = r/V measures how quickly the water in the lake is replaced through inflow
Repeat Exercise 1 for Lake Superior.Data from exercises 1Calculate the number of years to reduce pollution in Lake Erie to each level.40%30%
In Exercise 1, how long will it take Kimberly to accumulate $30,000 in her retirement account?Data from Exercises 1Kimberly Austin deposits $5000 in an IRA at 6% interest compounded continuously for
Repeat Exercise 1 for Lake Michigan.Data from exercises 1Calculate the number of years to reduce pollution in Lake Erie to each level.40%30% The following figures, representing years, were found in
Kimberly Austin deposits $5000 in an IRA at 6% interest compounded continuously for her retirement in 10 years. She intends to make continuous deposits at the rate of $3000 a year until she retires.
Calculate the number of years to reduce pollution in Lake Erie to each level.a. 40%b. 30% The following figures, representing years, were found in this way. Fortunately, the pollution in Lake
Evaluate each iterated integral. (1²3 - dx dy X

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