Multivariable Calculus
11th Edition
ISBN: 9781337275378
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Chapter 16, Problem 5RE
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Chapter 16 Solutions
Multivariable Calculus
Ch. 16.1 - Exactness What does it mean for the...Ch. 16.1 - Integrating Factor When is it beneficial to use an...Ch. 16.1 - Testing for Exactness In Exercises 3-6, determine...Ch. 16.1 - Testing for Exactness In Exercises 3-6, determine...Ch. 16.1 - Prob. 5ECh. 16.1 - Prob. 6ECh. 16.1 - Prob. 7ECh. 16.1 - Solving an Exact Differential Equation In...Ch. 16.1 - Prob. 9ECh. 16.1 - Prob. 10E
Ch. 16.1 - Prob. 11ECh. 16.1 - Prob. 12ECh. 16.1 - Prob. 13ECh. 16.1 - Prob. 14ECh. 16.1 - Prob. 15ECh. 16.1 - Graphical and Analytic AnalysisIn Exercises 15 and...Ch. 16.1 - Prob. 17ECh. 16.1 - Prob. 18ECh. 16.1 - Prob. 19ECh. 16.1 - Finding a Particular SolutionIn Exercises 17-22,...Ch. 16.1 - Prob. 21ECh. 16.1 - Prob. 22ECh. 16.1 - Prob. 23ECh. 16.1 - Prob. 24ECh. 16.1 - Prob. 25ECh. 16.1 - Prob. 26ECh. 16.1 - Prob. 27ECh. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Prob. 29ECh. 16.1 - Prob. 30ECh. 16.1 - Prob. 31ECh. 16.1 - Prob. 32ECh. 16.1 - Prob. 33ECh. 16.1 - Using an Integrating Factor In Exercises 33-36,...Ch. 16.1 - Prob. 35ECh. 16.1 - Prob. 36ECh. 16.1 - Prob. 37ECh. 16.1 - Prob. 38ECh. 16.1 - Tangent Curves In Exercises 39-42, use agraphing...Ch. 16.1 - Prob. 40ECh. 16.1 - Prob. 41ECh. 16.1 - Prob. 42ECh. 16.1 - Prob. 43ECh. 16.1 - Finding an Equation of a Curve In Exercises 43 and...Ch. 16.1 - Cost In a manufacturing process where y=C(x)...Ch. 16.1 - HOW DO YOU SEE? The graph shows several...Ch. 16.1 - Prob. 47ECh. 16.1 - Prob. 48ECh. 16.1 - Prob. 49ECh. 16.1 - Prob. 50ECh. 16.1 - Prob. 51ECh. 16.1 - Prob. 52ECh. 16.1 - Prob. 53ECh. 16.1 - Prob. 54ECh. 16.1 - Prob. 55ECh. 16.1 - Prob. 56ECh. 16.1 - Prob. 57ECh. 16.1 - Prob. 58ECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5ECh. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.2 - Prob. 8ECh. 16.2 - Prob. 9ECh. 16.2 - Prob. 10ECh. 16.2 - Prob. 11ECh. 16.2 - Prob. 12ECh. 16.2 - Prob. 13ECh. 16.2 - Prob. 14ECh. 16.2 - Prob. 15ECh. 16.2 - Prob. 16ECh. 16.2 - Prob. 17ECh. 16.2 - Prob. 18ECh. 16.2 - Prob. 19ECh. 16.2 - Prob. 20ECh. 16.2 - Prob. 21ECh. 16.2 - Prob. 22ECh. 16.2 - Prob. 23ECh. 16.2 - Prob. 24ECh. 16.2 - Prob. 25ECh. 16.2 - Prob. 26ECh. 16.2 - Prob. 27ECh. 16.2 - Prob. 28ECh. 16.2 - Prob. 29ECh. 16.2 - Prob. 30ECh. 16.2 - Prob. 31ECh. 16.2 - Finding a General Solution In exercises 9-36, find...Ch. 16.2 - Prob. 33ECh. 16.2 - Prob. 34ECh. 16.2 - Prob. 35ECh. 16.2 - Prob. 36ECh. 16.2 - Prob. 37ECh. 16.2 - Finding a Particular Solution Determine C and ...Ch. 16.2 - Prob. 39ECh. 16.2 - Prob. 40ECh. 16.2 - Prob. 41ECh. 16.2 - Find a Particular Solution: Initial ConditionsIn...Ch. 16.2 - Prob. 43ECh. 16.2 - Prob. 44ECh. 16.2 - Prob. 45ECh. 16.2 - Prob. 46ECh. 16.2 - Prob. 47ECh. 16.2 - Finding a Particular Solution: Boundary...Ch. 16.2 - Prob. 49ECh. 16.2 - Prob. 50ECh. 16.2 - Prob. 51ECh. 16.2 - Prob. 52ECh. 16.2 - Several shock absorbers are shown at the right. Do...Ch. 16.2 - Prob. 54ECh. 16.2 - Prob. 55ECh. 16.2 - Prob. 56ECh. 16.2 - Motion of a Spring In Exercise 55-58, match the...Ch. 16.2 - Prob. 58ECh. 16.2 - Prob. 59ECh. 16.2 - Prob. 60ECh. 16.2 - Prob. 61ECh. 16.2 - Prob. 62ECh. 16.2 - Prob. 63ECh. 16.2 - Prob. 64ECh. 16.2 - Prob. 65ECh. 16.2 - Prob. 66ECh. 16.2 - Prob. 67ECh. 16.2 - True or False? In exercises 67-70, determine...Ch. 16.2 - Prob. 69ECh. 16.2 - Prob. 70ECh. 16.2 - Wronskian The Wronskian of two differentiable...Ch. 16.2 - Prob. 72ECh. 16.2 - Prob. 73ECh. 16.2 - Prob. 74ECh. 16.3 - Prob. 1ECh. 16.3 - Choosing a MethodDetermine whether you woulduse...Ch. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.3 - Prob. 10ECh. 16.3 - Prob. 11ECh. 16.3 - Prob. 12ECh. 16.3 - Prob. 13ECh. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Prob. 15ECh. 16.3 - Prob. 16ECh. 16.3 - Prob. 17ECh. 16.3 - Prob. 18ECh. 16.3 - Prob. 19ECh. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Prob. 21ECh. 16.3 - Prob. 22ECh. 16.3 - Prob. 23ECh. 16.3 - Prob. 24ECh. 16.3 - Prob. 25ECh. 16.3 - Prob. 26ECh. 16.3 - Prob. 27ECh. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Prob. 29ECh. 16.3 - Electrical Circuits In Exercises 29 and 30, use...Ch. 16.3 - Prob. 31ECh. 16.3 - Prob. 32ECh. 16.3 - Prob. 33ECh. 16.3 - Prob. 34ECh. 16.3 - Prob. 35ECh. 16.3 - Prob. 36ECh. 16.3 - Prob. 37ECh. 16.3 - Prob. 38ECh. 16.3 - Prob. 39ECh. 16.3 - Prob. 40ECh. 16.3 - Prob. 41ECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Power Series Solution In Exercises 3-6, use a...Ch. 16.4 - Prob. 5ECh. 16.4 - Prob. 6ECh. 16.4 - Prob. 7ECh. 16.4 - Prob. 8ECh. 16.4 - Prob. 9ECh. 16.4 - Prob. 10ECh. 16.4 - Prob. 11ECh. 16.4 - Prob. 12ECh. 16.4 - Prob. 13ECh. 16.4 - Prob. 14ECh. 16.4 - Prob. 15ECh. 16.4 - Prob. 16ECh. 16.4 - Prob. 17ECh. 16.4 - Prob. 18ECh. 16.4 - Prob. 19ECh. 16.4 - Prob. 20ECh. 16.4 - Prob. 21ECh. 16.4 - Prob. 22ECh. 16.4 - Prob. 23ECh. 16.4 - Prob. 24ECh. 16.4 - Airys Equation Find the first six terms of the...Ch. 16 - Prob. 1RECh. 16 - Prob. 2RECh. 16 - Prob. 3RECh. 16 - Prob. 4RECh. 16 - Prob. 5RECh. 16 - Solving an Exact Differential Equation In...Ch. 16 - Prob. 7RECh. 16 - Prob. 8RECh. 16 - Prob. 9RECh. 16 - Prob. 10RECh. 16 - Prob. 11RECh. 16 - Prob. 12RECh. 16 - Prob. 13RECh. 16 - Prob. 14RECh. 16 - Prob. 15RECh. 16 - Prob. 16RECh. 16 - Prob. 17RECh. 16 - Prob. 18RECh. 16 - Prob. 19RECh. 16 - Prob. 20RECh. 16 - Prob. 21RECh. 16 - Prob. 22RECh. 16 - Prob. 23RECh. 16 - Prob. 24RECh. 16 - Prob. 25RECh. 16 - Prob. 26RECh. 16 - Prob. 27RECh. 16 - Prob. 28RECh. 16 - Prob. 29RECh. 16 - Prob. 30RECh. 16 - Prob. 31RECh. 16 - Prob. 32RECh. 16 - Prob. 33RECh. 16 - Prob. 34RECh. 16 - Prob. 35RECh. 16 - Motion of a SpringIn Exercise 35-36, a 64-pound...Ch. 16 - Prob. 37RECh. 16 - Prob. 38RECh. 16 - Prob. 39RECh. 16 - Prob. 40RECh. 16 - Prob. 41RECh. 16 - Prob. 42RECh. 16 - Prob. 43RECh. 16 - Prob. 44RECh. 16 - Prob. 45RECh. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Prob. 47RECh. 16 - Prob. 48RECh. 16 - Prob. 49RECh. 16 - Prob. 50RECh. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Prob. 52RECh. 16 - Prob. 53RECh. 16 - Prob. 54RECh. 16 - Prob. 55RECh. 16 - Prob. 56RECh. 16 - Prob. 57RECh. 16 - Prob. 58RECh. 16 - Prob. 59RECh. 16 - Prob. 60RECh. 16 - Prob. 61RECh. 16 - Prob. 62RECh. 16 - Prob. 1PSCh. 16 - Prob. 2PSCh. 16 - Prob. 3PSCh. 16 - Prob. 4PSCh. 16 - Prob. 5PSCh. 16 - Prob. 6PSCh. 16 - Prob. 7PSCh. 16 - Prob. 8PSCh. 16 - Pendulum Consider a pendulum of length L that...Ch. 16 - Prob. 10PSCh. 16 - Prob. 11PSCh. 16 - Prob. 12PSCh. 16 - Prob. 13PSCh. 16 - Prob. 14PSCh. 16 - Prob. 15PSCh. 16 - ChebyshevsEquation ConsiderChebyshevs equation...Ch. 16 - Prob. 17PSCh. 16 - Prob. 18PSCh. 16 - Prob. 19PSCh. 16 - Laguerres Equation Consider Laguerres Equation...
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- f'(x)arrow_forwardA body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.arrow_forwardA chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as: dx/dt = k(a-x)(b-x) where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?arrow_forwardConsider a body of mass m dropped from rest at t = 0. The body falls under the influence of gravity, and the air resistance FD opposing the motion is assumed to be proportional to the square of the velocity, so that FD = kV2. Call x the vertical distance and take the positive direction of the x-axis downward, with origin at the initial position of the body. Obtain relationships for the velocity and position of the body as a function of time t.arrow_forwardAssuming that the rate of change of the price P of a certain commodity is proportional to the difference between demand D and supply S at any time t, the differential equations describing the price fluctuations with respect to time can be expressed as: dP/dt = k(D - s) where k is the proportionality constant whose value depends on the specific commodity. Solve the above differential equation by expressing supply and demand as simply linear functions of price in the form S = aP - b and D = e - fParrow_forwardFind the area of the surface obtained by rotating the circle x² + y² = r² about the line y = r.arrow_forward1) Find the equation of the tangent line to the graph y=xe at the point (1, 1).arrow_forward3) Suppose that f is differentiable on [0, 5], and f'(x) ≤ 3 over this interval. If f(0) = −1, what is the maximum possible value of f(5)?arrow_forward2) Find the maximum value of f(x, y) = x - y on the circle x² + y² - 4x - 2y - 4 = 0.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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