Calculus: Early Transcendentals (2nd Edition)
2nd Edition
ISBN: 9780321947345
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
Publisher: PEARSON
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Chapter D1.2, Problem 39E
a.
To determine
To Find: The equilibrium solution for the given
b.
To determine
To sketch: The direction field for the given differential equation.
c.
To determine
To sketch: The direction field with the given initial condition that is
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3.9 (A/B). A beam ABCDE, with A on the left, is 7 m long and is simply supported at
Band E. The lengths of the various portions are AB 1-5m, BC = 1-5m, CD = 1 m and DE
: 3 m. There is a uniformly distributed load of 15kN/m between B and a point 2m
to the right of B and concentrated loads of 20 KN act at 4 and 0 with one of 50
KN at C. (a) Draw the S.F. diagrams and hence determine the position from A at
which the S.F. is zero. (b) Determine the value of the B.M. at this point. (c) Sketch
the B.M. diagram approximately to scale, quoting the principal values. [3.32 m, 69.8
KNm, 0, 30, 69.1, 68.1, 0 kNm.]
4. Verify that V X (aẢ) = (Va) XẢ +
aV X Ả where Ả = xyz(x + y + 2)
A
and a = 3xy + 4zx by carrying out
the detailed differentiations.
Chapter D1 Solutions
Calculus: Early Transcendentals (2nd Edition)
Ch. D1.1 - Prob. 1ECh. D1.1 - Prob. 2ECh. D1.1 - Prob. 3ECh. D1.1 - If the general solution of a differential equation...Ch. D1.1 - Does the function y(t) = 2t satisfy the...Ch. D1.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...
Ch. D1.1 - Verifying solutions of initial value problems...Ch. D1.1 - Verifying solutions of initial value problems...Ch. D1.1 - Verifying solutions of initial value problems...Ch. D1.1 - Verifying solutions of initial value problems...Ch. D1.1 - Finding general solutions Find the general...Ch. D1.1 - Finding general solutions Find the general...Ch. D1.1 - Finding general solutions Find the general...Ch. D1.1 - Finding general solutions Find the general...Ch. D1.1 - Finding general solutions Find the general...Ch. D1.1 - Finding general solutions Find the general...Ch. D1.1 - Finding general solutions Find the general...Ch. D1.1 - Prob. 22ECh. D1.1 - Solving initial value problems Solve the following...Ch. D1.1 - Solving initial value problems Solve the following...Ch. D1.1 - Solving initial value problems Solve the following...Ch. D1.1 - Solving initial value problems Solve the following...Ch. D1.1 - Solving initial value problems Solve the following...Ch. D1.1 - Solving initial value problems Solve the following...Ch. D1.1 - Motion in a gravitational field An object is fired...Ch. D1.1 - Prob. 30ECh. D1.1 - Prob. 31ECh. D1.1 - Prob. 32ECh. D1.1 - Prob. 33ECh. D1.1 - Prob. 34ECh. D1.1 - Explain why or why not Determine whether the...Ch. D1.1 - General solutions Find the general solution of the...Ch. D1.1 - General solutions Find the general solution of the...Ch. D1.1 - General solutions Find the general solution of the...Ch. D1.1 - General solutions Find the general solution of the...Ch. D1.1 - Solving initial value problems Find the solution...Ch. D1.1 - Solving initial value problems Find the solution...Ch. D1.1 - Solving initial value problems Find the solution...Ch. D1.1 - Solving initial value problems Find the solution...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - A second-order equation Consider the differential...Ch. D1.1 - Another second-order equation Consider the...Ch. D1.1 - Drug infusion The delivery of a drug (such as an...Ch. D1.1 - Logistic population growth Widely used models for...Ch. D1.1 - Free fall One possible model that describes the...Ch. D1.1 - Chemical rate equations The reaction of certain...Ch. D1.1 - Tumor growth The growth of cancer tumors may be...Ch. D1.2 - Explain how to sketch the direction field of the...Ch. D1.2 - Prob. 2ECh. D1.2 - Prob. 3ECh. D1.2 - Prob. 4ECh. D1.2 - Direction fields A differential equation and its...Ch. D1.2 - Prob. 6ECh. D1.2 - Identifying direction fields Which of the...Ch. D1.2 - Prob. 9ECh. D1.2 - Prob. 10ECh. D1.2 - Direction fields with technology Plot a direction...Ch. D1.2 - Sketching direction fields Use the window [2, 2] ...Ch. D1.2 - Sketching direction fields Use the window [2, 2] ...Ch. D1.2 - Sketching direction fields Use the window [2, 2] ...Ch. D1.2 - Sketching direction fields Use the window [2, 2] ...Ch. D1.2 - Sketching direction fields Use the window [2, 2] ...Ch. D1.2 - Increasing and decreasing solutions Consider the...Ch. D1.2 - Increasing and decreasing solutions Consider the...Ch. D1.2 - Increasing and decreasing solutions Consider the...Ch. D1.2 - Increasing and decreasing solutions Consider the...Ch. D1.2 - Logistic equations Consider the following logistic...Ch. D1.2 - Logistic equations Consider the following logistic...Ch. D1.2 - Logistic equations Consider the following logistic...Ch. D1.2 - Logistic equations Consider the following logistic...Ch. D1.2 - Two steps of Eulers method For the following...Ch. D1.2 - Two steps of Eulers method For the following...Ch. D1.2 - Two steps of Eulers method For the following...Ch. D1.2 - Two steps of Eulers method For the following...Ch. D1.2 - Errors in Eulers method Consider the following...Ch. D1.2 - Errors in Eulers method Consider the following...Ch. D1.2 - Prob. 31ECh. D1.2 - Prob. 32ECh. D1.2 - Prob. 33ECh. D1.2 - Prob. 34ECh. D1.2 - Prob. 35ECh. D1.2 - Prob. 36ECh. D1.2 - Prob. 37ECh. D1.2 - Equilibrium solutions A differential equation of...Ch. D1.2 - Prob. 39ECh. D1.2 - Prob. 40ECh. D1.2 - Equilibrium solutions A differential equation of...Ch. D1.2 - Equilibrium solutions A differential equation of...Ch. D1.2 - Direction field analysis Consider the first-order...Ch. D1.2 - Eulers method on more general grids Suppose the...Ch. D1.2 - Prob. 46ECh. D1.2 - Prob. 47ECh. D1.2 - Prob. 48ECh. D1.2 - Convergence of Eulers method Suppose Eulers method...Ch. D1.2 - Stability of Eulers method Consider the initial...Ch. D1.3 - What is a separable first-order differential...Ch. D1.3 - Is the equation t2y(t)=t+4y2 separable?Ch. D1.3 - Is the equation y(t)=2yt separable?Ch. D1.3 - Explain how to solve a separable differential...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Solving separable equations Find the general...Ch. D1.3 - Prob. 17ECh. D1.3 - Solving initial value problems Determine whether...Ch. D1.3 - Solving initial value problems Determine whether...Ch. D1.3 - Solving initial value problems Determine whether...Ch. D1.3 - Solving initial value problems Determine whether...Ch. D1.3 - Solving initial value problems Determine whether...Ch. D1.3 - Prob. 23ECh. D1.3 - Prob. 24ECh. D1.3 - Solving initial value problems Determine whether...Ch. D1.3 - Solving initial value problems Determine whether...Ch. D1.3 - Prob. 27ECh. D1.3 - Solutions in implicit form Solve the following...Ch. D1.3 - Solutions in implicit form Solve the following...Ch. D1.3 - Solutions in implicit form Solve the following...Ch. D1.3 - Prob. 31ECh. D1.3 - Solutions in implicit form Solve the following...Ch. D1.3 - Logistic equation for a population A community of...Ch. D1.3 - Logistic equation for an epidemic When an infected...Ch. D1.3 - Explain why or why not Determine whether the...Ch. D1.3 - Prob. 36ECh. D1.3 - Prob. 37ECh. D1.3 - Prob. 38ECh. D1.3 - Solutions of separable equations Solve the...Ch. D1.3 - Prob. 40ECh. D1.3 - Implicit solutions for separable equations For the...Ch. D1.3 - Orthogonal trajectories Two curves are orthogonal...Ch. D1.3 - Prob. 43ECh. D1.3 - Applications 44.Logistic equation for spread of...Ch. D1.3 - Free fall An object in free fall may be modeled by...Ch. D1.3 - Prob. 46ECh. D1.3 - Prob. 47ECh. D1.3 - Chemical rate equations Let y(t) be the...Ch. D1.3 - Prob. 49ECh. D1.3 - Blowup in finite time Consider the initial value...Ch. D1.3 - Prob. 52ECh. D1.3 - Analysis of a separable equation Consider the...Ch. D1.4 - The general solution of a first-order linear...Ch. D1.4 - Prob. 2ECh. D1.4 - What is the general solution of the equation y'(t)...Ch. D1.4 - Prob. 4ECh. D1.4 - First-order linear equations Find the general...Ch. D1.4 - First-order linear equations Find the general...Ch. D1.4 - First-order linear equations Find the general...Ch. D1.4 - First-order linear equations Find the general...Ch. D1.4 - First-order linear equations Find the general...Ch. D1.4 - First-order linear equations Find the general...Ch. D1.4 - Initial value problems Solve the following initial...Ch. D1.4 - Initial value problems Solve the following initial...Ch. D1.4 - Initial value problems Solve the following initial...Ch. D1.4 - Initial value problems Solve the following initial...Ch. D1.4 - Initial value problems Solve the following initial...Ch. D1.4 - Initial value problems Solve the following initial...Ch. D1.4 - Stability of equilibrium points Find the...Ch. D1.4 - Stability of equilibrium points Find the...Ch. D1.4 - Stability of equilibrium points Find the...Ch. D1.4 - Stability of equilibrium points Find the...Ch. D1.4 - Stability of equilibrium points Find the...Ch. D1.4 - Stability of equilibrium points Find the...Ch. D1.4 - Loan problems The following initial value problems...Ch. D1.4 - Loan problems The following initial value problems...Ch. D1.4 - Loan problems The following initial value problems...Ch. D1.4 - Loan problems The following initial value problems...Ch. D1.4 - Newtons Law of Cooling Solve the differential...Ch. D1.4 - Newton's Law of Cooling Solve the differential...Ch. D1.4 - Newtons Law of Cooling Solve the differential...Ch. D1.4 - Prob. 30ECh. D1.4 - Explain why or why not Determine whether the...Ch. D1.4 - Prob. 32ECh. D1.4 - Special equations A special class of first-order...Ch. D1.4 - Prob. 34ECh. D1.4 - Special equations A special class of first-order...Ch. D1.4 - Prob. 36ECh. D1.4 - A bad loan Consider a loan repayment plan...Ch. D1.4 - Prob. 38ECh. D1.4 - Intravenous drug dosing The amount of drug in the...Ch. D1.4 - Optimal harvesting rate Let y(t) be the population...Ch. D1.4 - Endowment model An endowment is an investment...Ch. D1.4 - Prob. 43ECh. D1.4 - Prob. 44ECh. D1.4 - General first-order linear equations Consider the...Ch. D1.4 - Prob. 46ECh. D1.4 - Prob. 47ECh. D1.4 - General first-order linear equations Consider the...Ch. D1.5 - Explain how the growth rate function determines...Ch. D1.5 - Prob. 2ECh. D1.5 - Explain how the growth rate function can be...Ch. D1.5 - Prob. 4ECh. D1.5 - Is the differential equation that describes a...Ch. D1.5 - What are the assumptions underlying the...Ch. D1.5 - Describe the solution curves in a predator-prey...Ch. D1.5 - Prob. 8ECh. D1.5 - Solving logistic equations Write a logistic...Ch. D1.5 - Solving logistic equations Write a logistic...Ch. D1.5 - Designing logistic functions Use the method of...Ch. D1.5 - Designing logistic functions Use the method of...Ch. D1.5 - Prob. 19ECh. D1.5 - Prob. 20ECh. D1.5 - Solving the Gompertz equation Solve the Gompertz...Ch. D1.5 - Prob. 22ECh. D1.5 - Stirred tank reactions For each of the following...Ch. D1.5 - Prob. 24ECh. D1.5 - Prob. 25ECh. D1.5 - Prob. 26ECh. D1.5 - Prob. 31ECh. D1.5 - Growth rate functions a.Show that the logistic...Ch. D1.5 - Solution of the logistic equation Use separation...Ch. D1.5 - Properties of the Gompertz solution Verify that...Ch. D1.5 - Properties of stirred tank solutions a.Show that...Ch. D1.5 - Prob. 36ECh. D1.5 - RC circuit equation Suppose a battery with voltage...Ch. D1.5 - U.S. population projections According to the U.S....Ch. D1 - Explain why or why not Determine whether the...Ch. D1 - Prob. 2RECh. D1 - General solutions Use the method of your choice to...Ch. D1 - General solutions Use the method of your choice to...Ch. D1 - General solutions Use the method of your choice to...Ch. D1 - Prob. 6RECh. D1 - General solutions Use the method of your choice to...Ch. D1 - General solutions Use the method of your choice to...Ch. D1 - General solutions Use the method of your choice to...Ch. D1 - Prob. 10RECh. D1 - Solving initial value problems Use the method of...Ch. D1 - Prob. 12RECh. D1 - Solving initial value problems Use the method of...Ch. D1 - Prob. 14RECh. D1 - Solving initial value problems Use the method of...Ch. D1 - Solving initial value problems Use the method of...Ch. D1 - Prob. 17RECh. D1 - Solving initial value problems Use the method of...Ch. D1 - Direction fields Consider the direction field for...Ch. D1 - Prob. 20RECh. D1 - Eulers method Consider the initial value problem...Ch. D1 - Equilibrium solutions Find the equilibrium...Ch. D1 - Equilibrium solutions Find the equilibrium...Ch. D1 - Equilibrium solutions Find the equilibrium...Ch. D1 - Equilibrium solutions Find the equilibrium...Ch. D1 - Logistic growth The population of a rabbit...Ch. D1 - Logistic growth parameters A cell culture has a...Ch. D1 - Logistic growth in India The population of India...Ch. D1 - Stirred tank reaction A 100-L tank is filled with...Ch. D1 - Newtons Law of Cooling A cup of coffee is removed...Ch. D1 - A first-order equation Consider the equation...Ch. D1 - A second-order equation Consider the equation...
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- 3. For each of the arrow or quiver graphs shown below, determine analytically V°C and V X Č. From these analytical solutions, identify the extrema (+/-) and plot these points on the arrow graph. (a) C = −✰CosxSiny + ŷSinxCosy -π<ׂу<π Ty (b) C = −xSin2y + ŷCos2y x, y<π -π< (c) C = −xCosx + ŷSiny -π< x, y < πarrow_forward7.10 (B/C). A circular flat plate of diameter 305 mm and thickness 6.35 mm is clamped at the edges and subjected to a Uniform lateral pressure of 345 kN/m². Evaluate: (a) the central deflection, (b) the position and magnitude of the maximum radial stress. C6.1 x 10 m; 149.2 MN/m².] 100 200arrow_forward3.15 (B). A beam ABCD is simply supported at B and C with ABCD=2m; BC 4 m. It carries a point load of 60 KN at the free end A, a Uniformly distributed load of 60 KN/m between B and C and an anticlockwise moment of 80 KN m in the plane of the beam applied at the free end D. Sketch and dimension the S.F. and B.M. diagrams, and determine the position and magnitude of the maximum bending moment. CEL.E.] CS.F. 60, 170, 70KN, B.M. 120, +120.1, +80 kNm, 120.1 kNm at 2.83 m to right of 8.7arrow_forward
- 7.1 (A/B). A Uniform I-section beam has flanges 150 mm wide by 8 mm thick and a web 180 mm wide and 8 mm thick. At a certain section there is a shearing force of 120 KN. Draw a diagram to illustrate the distribution of shear stress across the section as a result of bending. What is the maximum shear stress? [86.7 MN/m².arrow_forward1. Let Ả = −2x + 3y+42, B = - - 7x +lý +22, and C = −1x + 2y + 42. Find (a) Ả X B (b) ẢX B°C c) →→ Ả B X C d) ẢB°C e) ẢX B XC.arrow_forward3.13 (B). A beam ABC, 6 m long, is simply-supported at the left-hand end A and at B I'm from the right-hand end C. The beam is of weight 100 N/metre run. (a) Determine the reactions at A and B. (b) Construct to scales of 20 mm = 1 m and 20 mm = 100 N, the shearing-force diagram for the beam, indicating thereon the principal values. (c) Determine the magnitude and position of the maximum bending moment. (You may, if you so wish, deduce the answers from the shearing force diagram without constructing a full or partial bending-moment diagram.) [C.G.] C240 N, 360 N, 288 Nm, 2.4 m from A.]arrow_forward
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