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study help
mathematics
precalculus
Calculus Of A Single Variable 11th Edition Ron Larson, Bruce H. Edwards - Solutions
Find Mx, My, and (x̅,y̅) for the lamina of uniform density ρ bounded by the graphs of the equations.y = -x2 + 4x + 2, y = x + 2
Economists use Lorenz curves to illustrate the distribution of income in a country. A Lorenz curve, y = f (x), represents the actual income distribution in the country. In this model, x represents percents of families in the country from the poorest to the wealthiest and y represents percents of
Find the area of the given region bounded by the graphs of y1, y2, and y3, as shown in the figure.y1 = sin x, y2 = cos x, y3 = sin x + cos x 2 Y3 3 14 Figure for 52 Y/₂ IN 2 Yı x
Sketch the region bounded by the graphs of the equations and find the area of the region.f(x) = xe-x2, y = 0, 0 ≤ x ≤ 1
Write and evaluate the definite integral that represents the area of the region bounded by the graph of the function and the tangent line to the graph at the given point.f(x) = x - x3, (-1, 0)
Write and evaluate the definite integral that represents the area of the region bounded by the graph of the function and the tangent line to the graph at the given point.f(x) = 2x3 - 1, (1, 1)
Use integration to find the area of the figure having the given vertices.(-1, -1), (1, 1), (2, -1)
Sketch the region bounded by the graphs of the equations and find the area of the region.f(x) = 1/9x2, y = 1, x = 1, x = 2
Sketch the region bounded by the graphs of the equations and find the area of the region.f(x) = -2x, g(x) = 1 - 3x
Sketch the region bounded by the graphs of the equations and find the area of the region.f(x) = -4/x3, y = 0, x = -3, x = -1
Sketch a region for which integration with respect to y is easier than integration with respect to x.
Explain why it is important to determine all points of intersection of two curves when finding the area of the region between the curves.
Describe how to find the area of the region bounded by the graphs of f (x) and g(x) and the vertical lines x = a and x = b, where f and g do not intersect on [a, b].
What is the geometric interpretation of the area of the region between two curves?
Let S represent sales of a new product (in thousands of units), let L represent the maximum level of sales (in thousands of units), and let t represent time (in months). The rate of change of S with respect to t is proportional to the product of S and L - S.(a) Write the differential equation for
(a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.(b) Evaluate the limit, using L’Hôpital’s Rule if necessary.(c) Use a graphing utility to graph the function and verify the result in part (b).limx ∞ (ex - x)
Find the derivative of the function.f (x) = arcsin(x - 1)
Find the derivative of the function.h(t) = log5(4 - t)2
Determine whether each differential equation is separable.(a) y = 2x5 y' - y'(b) y' /x = x2 y + 1
Describe how to determine whether a function y = f (x) is a solution of a differential equation.
What does it mean for two families of curves to be mutually orthogonal?
For y = Cekt, explain why exponential growth occurs when k > 0 and exponential decay occurs when k < 0.
Use integration to find a general solution of the differential equation.dy/dx = 4x2 + 7
Describe carrying capacity in your own words.
What do the line segments on a slope field represent?
Find the general solution of the differential equation.dy/dx = x + 3
Find the general solution of the differential equation.dy/dx = 5 - 8x
Although it is true for some functions f and g, a common mistake in calculus is to believe that the Product Rule for derivatives is (fg)' = f'g'.(a) Given g(x) = x, find f such that (fg)' = f'g'.(b) Given an arbitrary function g, find a function f such that (fg)' = f'g'.(c) Describe what happens if
Use integration to find a general solution of the differential equation.dy/dx = 6 - x/3x, x > 0
List a real-life application that can be modeled by the logistic differential equation.
What does Euler’s Method allow you to do?
Find the general solution of the differential equation.dy/dx = y + 3
Find the general solution of the differential equation.dy/dx = x/y
Find the general solution of the differential equation.dy/dx = 6 - y
Use integration to find a general solution of the differential equation.dy/dx = 8 csc x cot x
Find the general solution of the differential equation.dy/dx = 3x2/y2
Find the general solution of the differential equation.y' = 5x/y
Use integration to find a general solution of the differential equation.dy/dx = e2 - x
Find the general solution of the first-order linear differential equation for x > 0.dy/dx + (1/x) y = 6x + 2
Find the general solution of the differential equation.dy/dx = x - 1/y3
Find the general solution of the differential equation.y' = -√x/4y
Use integration to find a general solution of the differential equation.dy/dx = 2e3x
Find the general solution of the first-order linear differential equation for x > 0.dy/dx + (2/x) y = 3x - 5
Find the general solution of the differential equation.dy/dx = 6 - x2/2y3
Find the general solution of the differential equation.y' = √x y
Find the general solution of the first-order linear differential equation for x > 0.y' + 2xy = 10x
Find the general solution of the differential equation.dr/ds = 4/9 r
What is the missing value? d dx -[sech ¹(3x)] = 3x√√1 - 9x²
Complete the table and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result.lim x∞ x5e-x/100 X f(x) 1 10 10² 10³ 104 105
Use the properties of logarithms to approximate the indicated logarithms, given that ln 4 = 1.3863 and ln 5 = 1.6094.(a) ln 0.0625(b) ln 5/4(c) ln 16(d) ln 3√80
(a) Let P(cos t, sin t) be a point on the unit circle x2 + y2 =1 in the first quadrant (see figure). Show that t is equal to twice the area of the shaded circular sector AOP.(b) Let P(cosh t, sinh t) be a point on the unit hyperbola x2 - y2 = 1 in the first quadrant (see figure). Show that t is
Evaluate the expression without using a calculator.log3 81
Evaluate the expression without using a calculator.arcsin 1/2
Evaluate the expression without using a calculator.arccos 1/2
Find the general solution of the differential equation.y' = x(1 + y)
Carriers are individuals who can transmit a disease but who exhibit no apparent symptoms. Let y represent the proportion of carriers in a population at any time t. Suppose that carriers are quarantined at a rate r. Then the change in the proportion of carriers can be modeled by dy/dt = -ry. Find
Find the general solution of the first-order linear differential equation for x > 0.y' + 3x2y = 6x2
Find the general solution of the differential equation.dr/ds = 9/4 s
Find the general solution of the differential equation.(1 + x2)y' - 2xy = 0
Find the general solution of the first-order linear differential equation for x > 0.(y + 1) cos x dx - dy = 0
Find the general solution of the differential equation.xy + y' = 100x
Find the general solution of the first-order linear differential equation for x > 0.(y - 1) sin x dx - dy = 0
Find the general solution of the differential equation.xy' = y
Find the general solution of the first-order linear differential equation for x > 0.y' + 3y = e3x
Find the general solution of the differential equation.y2y' = sin 9x
Find the general solution of the first-order linear differential equation for x > 0.xy' + y = x2 ln x
Find the general solution of the differential equation.yy' = -8 cos(πx)
Find the general solution of the differential equation.dy/dx = 6x - x3
Find the general solution of the differential equation.√1 - 4x2y' = x
Find the general solution of the differential equation.dy/dx = 3y + 5
Find the general solution of the differential equation.√x3 - 5y' = x2
Find the general solution of the differential equation.dy/dx = (y - 1)2
Find the general solution of the differential equation.dy/dx = x/x2 + 2
Find the general solution of the differential equation.12yy' - 7ex = 0
Find the general solution of the differential equation.(2 + x)y' - xy = 0
Find the general solution of the differential equation.xy' - (x + 1)y = 0
Find the general solution of the differential equation.√x + 1y' - y = 0
Use Example 1 as a model to evaluate the limit over the region bounded by the graphs of the equations. Example 1 lim Σ.f(c) Δx; το i=1
Find the general solution of the differential equation.y' + √xy = 9√x
Find an equation of the curve that passes through the point and has the given slope.(3, 1), y' = - y/5x
Use Example 1 as a model to evaluate the limit over the region bounded by the graphs of the equations. Example 1 lim Σ.f(c) Δx; το i=1
Consider an object with a mass of 4 kilograms dropped from a height of 1500 meters, where the air resistance is proportional to the velocity.Write the velocity of the object as a function of time t when the velocity after 5 seconds is approximately -31 meters per second. What is the limiting value
Find an equation of the curve that passes through the point and has the given slope.(8, 2), y' = 2y/3x
Find the balance in an account when $400 is deposited for 11 years at an interest rate of 2% compounded continuously.
The sales S (in thousands of units) of a new product after it has been on the market for t years is given by S = 25(1 - ekt).(a) Find S as a function of t when 4000 units have been sold after 1 year.(b) How many units will saturate this market?
Find the general solution of the differential equation.dy/dx = 5x/y
Find the general solution of the differential equation.dy/dx = x3/2y2
Find the orthogonal trajectories for the family of curves. Use a graphing utility to graph several members of each family.3x2 - y2 = C
The population (in millions) of a country in 2015 and the expected continuous annual rate of change k of the population are given. (a) Find the exponential growth model P = Cekt for the population by letting t = 5 correspond to 2015.(b) Use the model to predict the population of the country in
Find the general solution of the differential equation.y'ey - 3x = ex + 2y
The expression u(x) is an integrating factor for y' + P(x)y = Q(x). Which of the following is equal to u'(x)? Verify your answer.(a) P(x)u(x)(b) P'(x)u(x)(c) Q(x)u(x)(d) Q'(x)u(x)
The population (in millions) of a country in 2015 and the expected continuous annual rate of change k of the population are given. (a) Find the exponential growth model P = Cekt for the population by letting t = 5 correspond to 2015.(b) Use the model to predict the population of the country in
Explain why you can omit the constant of integration when finding an integrating factor.
Find the orthogonal trajectories for the family of curves. Use a graphing utility to graph several members of each family.5x2 - 4y2 = C
Find an equation of the curve that passes through the point and has the given slope.(1, 3), y' = 2x/y
Use integration to find a general solution of the differential equation.dy/dx = 3x8 - 2x
Use integration to find a general solution of the differential equation.dy/dx = 12x2
Find an equation of the curve that passes through the point and has the given slope.(1, -2), y' = y/8x
The value of a tract of timber is V(t) = 100,000e0.8√t where t is the time in years, with t = 0 corresponding to 2010. If money earns interest continuously at 10%, then the present value of the timber at any time t is A(t) = V(t)e-0.10t.Find the year in which the timber should be harvested to
Find the general solution of the first-order differential equation for x > 0 by any appropriate method.dy/dx = e2x + y/ex - y
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