All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Ask a Question

Search
Sign In
Register

study help
mathematics
applied calculus

Questions and Answers of Applied Calculus

Use the Fundamental Theorem to evaluate the definite integral exactly. 3 5 dx
Find the present and future values of an income stream of $2000 per year for 15 years, assuming a 5% interest rate compounded continuously.
Decide if the function is an antiderivative of f(x) = 2e2x.F(x) = 5e2x
Use the Fundamental Theorem to evaluate the definite integral exactly. S 0 6x dx
Find the consumer surplus for the demand curve p = 100−3q2 when q∗ = 5 units are sold at the equilibrium price.
The supply and demand curves for a product are given in Figure 6.40. Estimate the equilibrium price and quantity and the consumer and producer surplus. Shade areas representing the consumer surplus
Suppose f'(t) = (0.82)t and f(2) = 9. Find the value of f(b) for b = 2, 4, 6, 10, and 20.
Find the present and future values of an income stream of $12,000 a year for 20 years. The interest rate is 6%, compounded continuously.
Decide if the function is an antiderivative of f(x) = 2e2x.F(x) = e2x
Find the integrals in Problems. [test test dt
Suppose G'(t) = (1.12)t and G(5) = 1. Find the value of G(b) for b = 5, 5.1, 5.2, 5.5, and 6.0.
(a) What are the equilibrium price and quantity for the supply and demand curves in Figure 6.39?(b) Shade the areas representing the consumer and producer surplus and estimate them.
(a) Find the derivatives of sin(x2 + 1) and sin(x3 + 1).(b) Use your answer to part (a) to find antiderivatives of:(i) x cos(x2 + 1) (ii) x2 cos(x3 + 1)(c) Find the general antiderivatives of:(i) x
Figure 5.67 shows plasma concentration curves for two products containing a drug used to slow a rapid heart rate. Compare the two products in terms of level of peak concentration, time until peak
Draw a graph, with time in years on the horizontal axis, of what an income stream might look like for a company that sells sunscreen in the northeast United States.
Problems concern the future of the US Social Security Trust Fund, out of which pensions are paid. Figure 5.61 shows the rates (billions of dollars per year) at which income.I(t), from
A bicyclist pedals along a straight road with velocity, v, given in Figure 5.59. She starts 5 miles from a lake; positive velocities take her away from the lake and negative velocities take her
Decide if the function is an antiderivative of f(x) = 2e2x.F(x) = e2x + 5
“The crisis began around 10 am yesterday when a 10-foot wide pipe in Weston sprang a leak, which worsened throughout the afternoon and eventually cut off Greater Boston from the Quabbin Reservoir,
Use Figure 5.50 to find the values of(a) ∫20 f(x) dx(b) ∫73 f(x) dx(c) ∫72 f(x) dx(d) ∫85 f(x) dx 2 1 -1 -2 f(x) X 2 4 6 8 10 Figure 5.50: Graph consists of a semicircle and line segments
Suppose F'(x) = 2x2 + 5 and F(0) = 3. Find the value of F(b) for b = 0, 0.1, 0.2, 0.5, and 1.0.
Which of (I)–(V) are antiderivatives of f(x) = ex∕2?I. ex∕2 II. 2ex∕2 III. 2e(1+x)∕2IV. 2ex∕2 + 1V. ex2∕4
The demand curve for a product is given by q = 100−2p and the supply curve is given by q = 3p − 50.(a) Find the consumer surplus at the equilibrium.(b) Find the producer surplus at the
Let f(v) be the amount of energy consumed by a flying bird, measured in joules per second (a joule is a unit of energy), as a function of its speed v (in meters/sec). Let a(v) be the amount of energy
When birds lay eggs, they do so in clutches of several at a time. When the eggs hatch, each clutch gives rise to a brood of baby birds. We want to determine the clutch size which maximizes the number
The quantity of a drug in the bloodstream t hours after a tablet is swallowed is given, in mg, byq(t) = 20(e−t − e−2t).(a) How much of the drug is in the bloodstream at time t = 0?(b) When is
Investigate the one-parameter family of functions. Assume that a is positive.(a) Graph f(x) using three different values for a.(b) Using your graph in part (a), describe the critical points of f and
The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells in the blood:S = aHe−bH for positive constants a, b.(a) What value of H maximizes the oxygen
Investigate the one-parameter family of functions. Assume that a is positive.(a) Graph f(x) using three different values for a.(b) Using your graph in part (a), describe the critical points of f and
The number of offspring in a population may not be a linear function of the number of adults. The Ricker curve, used to model fish populations, claims that y = axe−bx, where x is the number of
Investigate the one-parameter family of functions. Assume that a is positive.(a) Graph f(x) using three different values for a.(b) Using your graph in part (a), describe the critical points of f and
During a flu outbreak in a school of 763 children, the number of infected children, I, was expressed in terms of the number of susceptible (but still healthy) children, S, by the functionWhat is the
On the west coast of Canada, crows eat whelks (a shellfish). To open the whelks, the crows drop them from the air onto a rock. If the shell does not smash the first time, the whelk is dropped again.
Find values of a and b so that f(x) = axebx has f(1∕3) = 1 and f has a local maximum at x = 1∕3.
(a) For a a positive constant, find all critical points of f(x) = x − a√x.(b) What value of a gives a critical point at x = 5? Does f(x) have a local maximum or a local minimum at this critical
An apple tree produces, on average, 400 kg of fruit each season. However, if more than 200 trees are planted per km2, crowding reduces the yield by 1 kg for each tree over 200.(a) Express the total
Sketch several members of the family y = x3 − ax2 on the same axes. Discuss the effect of the parameter a on the graph. Find all critical points for this function.
For what values of a and b does f(x) = a(x − b ln x) have a local minimum at the point (2, 5)? Figure 4.16 shows a graph of f(x) with a = 1 and b = 1. 3 2 1 f(x) = x-lnx 1 2 Figure 4.16 3 X
If you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
A rectangular swimming pool is to be built with an area of 1800 square feet. The owner wants 5-foot-wide decks along either side and 10-foot-wide decks at the two ends. Find the dimensions of the
Find the value of a so that f(x) = xeax has a critical point at x = 3.
The energy expended by a bird per day, E, depends on the time spent foraging for food per day, F hours. Foraging for a shorter time requires better territory, which then requires more energy for its
Find the exact global maximum and minimum values of the function. The domain is all real numbers unless otherwise specified. f(t) = 1 + f²
Suppose f has a continuous derivative whose values are given in the following table.(a) Estimate the x-coordinates of critical points of f for 0 ≤ x ≤ 10.(b) For each critical point, indicate if
Find constants a and b so that the minimum for the parabola f(x) = x2 + ax + b is at the given point.(−2, −3)
The impact of a drug is a measure of its effect, for example, the reduction in blood pressure, loss of weight, or the duration of a headache. The impact, I, generally depends on the dose, D, given.
Consumer demand for a product is changing over time, and the rate of change of demand, f'(t), in units/week, is given, in week t, for 0 ≤ t ≤ 10, in the following table.(a) When is the demand for
Find constants a and b so that the minimum for the parabola f(x) = x2 + ax + b is at the given point.(3, 5)
Figure 4.15 is a graph of f'. For what values of x does f have a local maximum? A local minimum? its 3 5 f'. Figure 4.15: Graph of f' (not f) x
(a) If a is a constant, find all critical points of f(x) = 5ax − 2x2.(b) Find the value of a so that f has a local maximum at x = 6.
What value of w minimizes S if S−5pw = 3qw2−6pq and p and q are positive constants?
(a) If a is a positive constant, find all critical points of f(x) = x3 − ax.(b) Find the value of a so that f has local extrema at x = ±2.
Find the exact global maximum and minimum values of the function. The domain is all real numbers unless otherwise specified.f(t) = (sin2 t + 2) cos t
The derivative of f(t) is given by f'(t) = t3 − 6t2 + 8t for 0 ≤ t ≤ 5. Graph f'(t), and describe how the function f(t) changes over the interval t = 0 to t = 5. When is f(t) increasing and
The function f is defined for all x. Use the graph of f' to decide:(a) Over what intervals is f increasing? Decreasing?(b) Does f have local maxima or minima? If so, which, and where? -1 f'(x) x
Find formulas for the functions described in Problems. a A function of the form y = 1 + be-¹ and an inflection point at t = 1. with y-intercept 2
Find the exact global maximum and minimum values of the function. The domain is all real numbers unless otherwise specified.f(x) = x − ln x for x > 0
The function f is defined for all x. Use the graph of f' to decide:(a) Over what intervals is f increasing? Decreasing?(b) Does f have local maxima or minima? If so, which, and where? 2 f'(x) 4 X
Find the exact global maximum and minimum values of the function. The domain is all real numbers unless otherwise specified.f(x) = e3x − e2x
Find the exact global maximum and minimum values of the function. The domain is all real numbers unless otherwise specified.f(x) = 2ex + 3e−x
The function f is defined for all x. Use the graph of f' to decide:(a) Over what intervals is f increasing? Decreasing?(b) Does f have local maxima or minima? If so, which, and where? f'(x) X
The vase in Figure 4.31 is filled with water at a constant rate (that is, constant volume per unit time).(a) Graph y = f(t), the depth of the water, against time, t. Show on your graph the points at
Find the exact global maximum and minimum values of the function. The domain is all real numbers unless otherwise specified.g(t) = te−t for t > 0
Find formulas for the functions described in Problems.A curve of the form y = e−(x−a)2∕b for b > 0 with a local maximum at x = 2 and points of inflection at x = 1 and x = 3.
The function f is defined for all x. Use the graph of f' to decide:(a) Over what intervals is f increasing? Decreasing?(b) Does f have local maxima or minima? If so, which, and where? X ((x) if |
Find the exact global maximum and minimum values of the function. The domain is all real numbers unless otherwise specified.f(x) = x + 1∕x for x > 0
If water is flowing at a constant rate (that is, constant volume per unit time) into the Grecian urn in Figure 4.30, sketch a graph of the depth of the water against time. Mark on the graph the time
Figure 4.14 is the graph of a derivative f'. On the graph, mark the x-values that are critical points of f. At which critical points does f have local maxima, local minima, or neither? f'(x) V Figure
Find the exact global maximum and minimum values of the function. The domain is all real numbers unless otherwise specified.g(x) = 4x − x2 − 5
Find formulas for the functions described in Problems.A cubic polynomial, ax3 + bx2 + cx+ d, with a critical point at x = 2, an inflection point at (1, 4), and a leading coefficient of 1.
The perimeter of a rectangle is 64 cm. Find the lengths of the sides of the rectangle giving the maximum area.
The sum of three nonnegative numbers is 36, and one of the numbers is twice one of the other numbers. What is the maximum value of the product of these three numbers?
If U and V are positive constants, find all critical points ofF(t) = Uet + V e−t.
Use the derivative to find all critical points. Assume that A, B, and C are positive constants.f(x) = Ax4 −Bx2 + C
(a) Water is flowing at a constant rate (i.e., constant volume per unit time) into a cylindrical container standing vertically. Sketch a graph showing the depth of water against time.(b) Water is
The product of two positive numbers is 784. What is the minimum value of their sum?
Use the derivative to find all critical points. Assume that A, B, and C are positive constants.f(x) = Ax3 − Bx
Find and classify the critical points of f(x) = x3(1−x)4 as local maxima and minima.
Indicate on Figure 4.28 approximately where the inflection points of f(x) are if the graph shows(a) The function f(x) (b) The derivative f¨(x)(c) The second derivative f¨¨(x) W Figure 4.28 X
Figure 4.42 shows a function f. Does f have a global maximum? A global minimum? If so, where? Assume that f(x) is defined for all x and that the graph does not change concavity outside the window
Problems concern f(t) in Figure 4.29, which gives the length of a human fetus as a function of its age.(a) What are the units of f¨(24)?(b) What is the biological meaning of f¨(24) = 1.6? length
Use the derivative to find all critical points. Assume that A, B, and C are positive constants.f(x) = Ax2 + Bx + C
Problems concern f(t) in Figure 4.29, which gives the length of a human fetus as a function of its age.(a) Which is greater, f¨(20) or f¨(36)?(b) What does your answer say about fetal growth?
Problems concern f(t) in Figure 4.29, which gives the length of a human fetus as a function of its age.(a) At what time does the inflection point occur?(b) What is the biological significance of this
The government imposes a tax of T dollars per item sold. The producers of the item react by raising the price to p dollars per item to consumers, which reduces the quantity of items sold to q
Figure 4.42 shows a derivative, f'. Does the function f have a global maximum? A global minimum? If so, where? Assume that f(x) and f¨(x) are defined for all x and that the graph of f¨(x) does not
A company manufactures only one product. The quantity, q, of this product produced per month depends on the amount of capital, K, invested (i.e., the number of machines the company owns, the size of
Problems concern f(t) in Figure 4.29, which gives the length of a human fetus as a function of its age.Estimate(a) f¨(20)(b) f¨(36)(c) The average rate of change of length over the 40 weeks shown.
A grapefruit is tossed straight up with an initial velocity of 50 ft/sec. The grapefruit is 5 feet above the ground when it is released. Its height, in feet, at time t seconds is given byy = −16t2
A company can produce and sell f(L) tons of a product per month using L hours of labor per month. The wage of the workers is w dollars per hour, and the finished product sells for p dollars per
Use the derivative to find all critical points. Assume that A, B, and C are positive constants.f(x) = C +Ax2 −Bx3
(a) A cruise line offers a trip for $2000 per passenger. If at least 100 passengers sign up, the price is reduced for all the passengers by $10 for every additional passenger (beyond 100) who goes on
The income elasticity of demand for a product is defined as Eincome = |I∕q ⋅ dq∕dI| where q is the quantity demanded as a function of the income I of the consumer. What does Eincome tell you
A business sells an item at a constant rate of r units per month. It reorders in batches of q units, at a cost of a + bq dollars per order. Storage costs are k dollars per item per month, and, on
The continuous function has exactly one critical point. Find the x-values at which the global maximum and the global minimum occur in the interval given.j¨(3) is undefined, j¨(x) = 2 for x < 3
For Problems sketch a possible graph of y = f(x), using the given information about the derivatives y¨ = f¨(x) and y¨¨ = f¨¨(x). Assume that the function is defined and continuous for all real
The function f(x) = x4 − 4x3 + 8x has a critical point at x = 1. Use the second-derivative test to identify it as a local maximum or local minimum.
Elasticity of cost with respect to quantity is defined as EC,q = q∕C ⋅ dC∕dq.(a) What does this elasticity tell you about sensitivity of cost to quantity produced?(b) Show that EC,q = Marginal
The continuous function has exactly one critical point. Find the x-values at which the global maximum and the global minimum occur in the interval given.ℎ¨(2) is undefined, ℎ¨(x) = −1 for x
For Problems sketch a possible graph of y = f(x), using the given information about the derivatives y' = f'(x) and y'' = f''(x). Assume that the function is defined and continuous for all real x. y =

Showing 600 - 700 of 5532

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Company Info

Security
Copyrights
Privacy Policy
Terms & Condition
SolutionInn Fee
Scholarship

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Copyright © 2024 SolutionInn All Rights Reserved.

Get the SolutionInn - Study Help App