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mathematics
calculus with applications

Questions and Answers of Calculus With Applications

Evaluate each iterated integral. 4 - dx dy ² 22 y
Find fxx(x, y) and fxy(x, y).f(x, y) = ln |1 + 3xy2|
Find fxx(x, y) and fxy(x, y).f(x, y) = ln|2 – x2y|
Find fxx(x, y) and fxy(x, y).f(x, y) = yex2
Find fx(x, y, z) ,fy(x, y, z), fz(x, y, z) and fyz(x, y, z) for the following.f(x, y, z) = 6x3 – x2y2 + y5
Evaluate each iterated integral. 1² fe 3 e2x-ly dx dy
Evaluate each iterated integral. 5 (6 32 V6x + 3y dx dy
Evaluate each iterated integral. L²L² (2x (2x + 6y + y2) dy dx
Evaluate each iterated integral 0 4 (x²y² + 5x) dx dy 0
A car dealership estimates that the total weekly sales of its most popular model is a function of the car’s list price, p, and the interest rate in percent, i, offered by the manufacturer. The
Suppose that the manufacturing cost of a personal digital assistant (PDA) is approximated by M(x, y) = 45x2 + 40y2 – 20xy + 50 where x is the cost of electronic chips and y is the cost of labor.
Find fxx(x, y) and fxy(x, y).f(x, y) = 4x2e2y
A company needs to construct a box with an open top that will be used to transport 400yd3 with an open top that will be used to transport of material, in several trips, from one place to another. Two
Find fxx(x, y) and fxy(x, y). f(x,y) 3x + y x-1
Find fxx(x, y) and fxy(x, y). f(x,y) = 3x 2х - у
Find fxx(x, y) and fxy(x, y).f(x, y) = –3x2y3 + x3y
Find fx(x, y, z) ,fy(x, y, z), fz(x, y, z) and fyz(x, y, z) for the following.f(x, y, z) = x4 + 2yz2 + z4
Find fxx(x, y) and fxy(x, y).f(x, y) = 5x3y – 6xy2
Find fx(x, y) and fy(x, y).f(x, y) = ln|2 – x2y3|
Find fx(x, y) and fy(x, y).f(x, y) = ln |2x2 + y2|
Find fx(x, y) and fy(x, y).f(x, y) = (y – 2)2ex+2y
Find fx(x, y) and fy(x, y).f(x, y) = x3e3y
Find fx(x, y) and fy(x, y). f(x, y) = 2x + 5y² 3x² + y²
Find fx(x, y) and fy(x, y). f(x, y) = √4x² + y²
Find fx(x, y) and fy(x, y).f(x, y) = 5x4y3 – 6x5y
Find fx(x, y) and fy(x, y).f(x, y) = 6x2y3 – 4y
Let Find the following. z = f(x, y) = x + y² 2. x-y
Let z = f(x, y) = 3x3 + 4x2y – 2y2. Find the following. a. az ax b. дz (-1,4) ду с. fху (2,-1)
Evaluate each iterated integral. 6x 1*11 ( 6²5 + 2) dx dy 3
Evaluate each iterated integral. -4 L L ( + 3) dx c dy
Evaluate each iterated integral. 1² ¹2 y dx dy
Evaluate each iterated integral. 3. xy dy dx
Evaluate each iterated integral. 25 7 3 + 5y Vx 16 2 dy dx
Evaluate each iterated integral. SA 93 + 5y √x 4 dx dy
Evaluate each iterated integral. -35 04 xVx² + 3y dy dx
Evaluate each iterated integral. -6 03 xVx² + 3y dx dy
Evaluate each iterated integral. f. f(x 0 (xy³ - x) dy dx
Graph the first-octant portion of each plane.z = 4
Evaluate each iterated integral. -25 [²(x²y + y) dx dy
Graph the first-octant portion of each plane.x = 5
Evaluate each integral. 5 ye+x+y¹² dx
Evaluate each integral. ye4x + y² dy
Evaluate each integral. L'e e2x+3y dy
Evaluate each integral. -6 2 e2x+3y dx
Evaluate each integral. 2 3 + 5y √x dy
Evaluate each integral. 4 3 + 5y Vx dx
Let Find the following.a. f(10, 2)b. f(100, 1)c. f(1000, 0)d. f(1/10, 5) f(x, y) = V9x + 5y log x
Evaluate each integral. 6 xVx² + 3y dx
Evaluate each integral. 5 4 xVx² + 3y dy
Evaluate each integral. (xy³ - x) dy
Evaluate each integral. [*(x³y + y) dx
Otis Taylor plots the price per share of a stock that he owns as a function of time and finds that it can be approximated by the function S(t) = t(25 – 5t) + 18, where t is the time (in years)
The Drucker family wants to establish an ongoing scholarship award at a college. Each year in June $3000 will be awarded, starting 1 year from now. What amount must the Druckers provide the college,
Suppose the number of items a new worker on an assembly line produces daily after t days on the job is given byFind the average number of items produced daily by this employee after the following
Using integration by parts,Subtracting ∫1/x dx from both sides we conclude that 0 = 1 What is wrong with this logic? 1 = = dx = 1/²/3 - 16 · dx X X 1 = — - - x - - / ( - 12/7) x dx X + f +/-
Find the average value of f(x) = √x + 1 over the interval [0, 8]
The booklet All About Lawns published by Ortho Books gives the following instructions for measuring the area of an irregularly shaped region. (See figure in the next column.)Irregular Shapes (within
In Exercises 24–28, estimate the area under each curve by summing the area of rectangles. Use the left endpoints, then the right endpoints, then give the average of those answers.The following
Find the following.∫(4/x3) dx
Find the following.∫(–9t–2.5 – 2t–1) dt
In Exercises 24–28, estimate the area under each curve by summing the area of rectangles. Use the left endpoints, then the right endpoints, then give the average of those answers.In 2001, the
Find the following.∫(10x–3.5 + 4x–1) dx
In Exercises 24–28, estimate the area under each curve by summing the area of rectangles. Use the left endpoints, then the right endpoints, then give the average of those answers.The graph shows
Find the following.∫1/3x2 dx
Find the following.∫2/3x4 dx
Canham Enterprises had an expenditure rate of E'(x) = e0.1x dollars per day and an income rate of I'(x) = 98.8 – e0.1x dollars per day on a particular job, where x was the number of days from the
A factory of Hollis Sherman Industries has installed a new process that will produce an increased rate of revenue (in thousands of dollars per year) ofwhere t is time measured in years. The new
Find the following.∫3e–0.2x dx
In 2001, the United Kingdom suffered an epidemic of foot-and-mouth disease. The graph below shows the reported number of cattle (red) and pigs (blue) that were culled each month from mid-February
Find the following.∫–4e0.2v dv
Estimate the distance traveled by the Mercedes-Benz S550, using the table below Acceleration Zero to 30 mph 40 mph 50 mph 60 mph 70 mph 80 mph 90 mph 100 mph 110 mph 120 mph 130
Find the following.∫(–3/x + 4e–0.4x + e0.1) dx
Estimate the distance traveled by the Chevrolet Malibu Maxx SS, using the table below. Acceleration Zero to 30 mph 40 mph 50 mph 60 mph 70 mph 80 mph 90 mph 100 mph 110
Find the following.∫(9/x – 3e–0.4x) dx
Find the following.∫(1 + 2t3)/4t dt
Find the following.∫2y1/2 – 3y2/6y dy
Find the following.∫(e2u + 4u) du
In 1987, Canadian Ben Johnson set a world record in the 100-m sprint. (The record was later taken away when he was found to have used an anabolic steroid to enhance his performance.) His speed at
In an article in the December 1994 Scientific American magazine, the authors estimated future gas use. Without a change in U.S. policy, auto fuel use is forecasted to rise along the projection shown
Find the following.∫(v2 – e3v)dv
Find the following.∫(2y – 1)2 dy
The following graph shows the number of vehicles per hour crossing the Tappan Zee Bridge, which spans the Hudson River north of New York City. The graph shows the number of vehicles traveling
The marginal revenue (in thousands of dollars) from the sale of x MP3 players is given by R´(x) = 4x(x2 + 27,000)–2/3.a. Find the total revenue function if the revenue from 125 players is
Find the following.∫10x dx
According to data from the Bureau of Transportation Statistics, the rate of change in the number of local transit vehicles (buses, light rail, etc.), in thousands, in the United States from 1970 to
According to data from the American Hospital Association, the rate of change in the number of hospital outpatient visits, in millions, in the United States each year from 1980 to the present can be
Find the following.∫32x dx
The approximate rate of change in the number (in billions) of monthly text messages is given by f´(t) = 7.50t – 16.8, where t represents the number of years since 2000. In 2005 (t = 5) there were
The number of bachelor’s degrees conferred in the United States has been increasing steadily in recent decades. Based on data from the National Center for Education Statistics, the rate of change
In Exercises 59–62, find the area between the x-axis and over each of the given intervals.f(x) = √4x – 3; [1, 3]
The number of degrees in dentistry (D.D.S. or D.M.D.) conferred to females in the United States has been increasing steadily in recent decades. Based on data from the National Center for Education
Based on data from the U.S. Census Bureau, an approximate family income distribution for the United States is given by the functionwhere x is the annual income in units of $10,000, with 0 ≤ x
Suppose that the rate of consumption of a natural resource is c(t), where c'(t) = kert. Here t is time in years, r is a constant, and k is the consumption in the year when t = 0. In 2010, an oil
The curve shown gives the rate that an investment accumulates income (in dollars per year). Use rectangles of width 2 units and height determined by the function value at the midpoint to find the
The function defined byapproximates marginal U.S. nonfarm productivity from 2000–2009. Productivity is measured as total output per hour compared to a measure of 100 for 2000, and x is the number
The rate of consumption of oil (in billions of barrels) by the company in Exercise 71 was given as 1.2e0.04t, where t = 0 corresponds to 2010. Find the total amount of oil used by the company from
The table on the next page shows the amount of property damage (in dollars) due to automobile accidents in California in recent years. In this exercise we are interested in the total amount of
Find dy/dx.x2 – 4y2 = 3x3y4
Find dy/dx.x2y3 + 4xy = 2
Find dy/dx.9√x + 4y3 = 2√y

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