Calculus Early Transcendentals, Binder Ready Version
11th Edition
ISBN: 9781118883822
Author: Howard Anton, Irl C. Bivens, Stephen Davis
Publisher: WILEY
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Chapter 15.1, Problem 10ES
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8–23. Sketching vector fields Sketch the following vector fields
25-30. Normal and tangential components For the vector field F and
curve C, complete the following:
a. Determine the points (if any) along the curve C at which the vector
field F is tangent to C.
b. Determine the points (if any) along the curve C at which the vector
field F is normal to C.
c. Sketch C and a few representative vectors of F on C.
25. F
=
(2½³, 0); c = {(x, y); y −
x² =
1}
26. F
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,
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27. F(x, y); C = {(x, y): x² + y² = 4}
28. F = (y, x); C = {(x, y): x² + y² = 1}
29. F = (x, y); C =
30. F = (y, x); C =
{(x, y): x = 1}
{(x, y): x² + y² = 1}
Chapter 15 Solutions
Calculus Early Transcendentals, Binder Ready Version
Ch. 15.1 - The function (x,y,z)=xy+yz+xz is a potential for...Ch. 15.1 - The vector field F(x,y,z)=, defined for...Ch. 15.1 - An inverse-square field is one that can be written...Ch. 15.1 - The vector field has divergence and curl
Ch. 15.1 - Match the vector field F(x,y) with one of the...Ch. 15.1 - Match the vector field F(x,y) with one of the...Ch. 15.1 - Determine whether the statement about the vector...Ch. 15.1 - Determine whether the statement about the vector...Ch. 15.1 - Sketch the vector field by drawing some...Ch. 15.1 - Sketch the vector field by drawing some...
Ch. 15.1 - Sketch the vector field by drawing some...Ch. 15.1 - Sketch the vector field by drawing some...Ch. 15.1 - Use a graphing utility to generate a plot of the...Ch. 15.1 - Use a graphing utility to generate a plot of the...Ch. 15.1 - Determine whether the statement is true or false....Ch. 15.1 - Determine whether the statement is true or false....Ch. 15.1 - Determine whether the statement is true or false....Ch. 15.1 - Determine whether the statement is true or false....Ch. 15.1 - Confirm that is a potential function for F(r) on...Ch. 15.1 - Confirm that is a potential function for F(r) on...Ch. 15.1 - Find div F and curl F . F(x,y,z)=x2i2j+yzkCh. 15.1 - Find div F and curl F . F(x,y,z)=xz3i+2y4x2j+5z2ykCh. 15.1 - Find div and curl .
Ch. 15.1 - Find div and curl .
Ch. 15.1 - Find div F and curl F ....Ch. 15.1 - Find div F and curl F ....Ch. 15.1 - Find(FG).F(x,y,z)=2xi+j+4ykG(x,y,z)=xi+yjzkCh. 15.1 - Find(FG).F(x,y,z)=yzi+xzj+xykG(x,y,z)=xyj+xyzkCh. 15.1 - Find(F).F(x,y,z)=sinxi+cos(xy)j+zkCh. 15.1 - Find(F).F(x,y,z)=exzi+3xeyjeyzkCh. 15.1 - Find(F).F(x,y,z)=xyj+xyzkCh. 15.1 - Find(F).F(x,y,z)=y2xi3yzj+xykCh. 15.1 - Use a CAS to check the calculations in Exercises...Ch. 15.1 - Use a CAS to check the calculations in Exercises...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Let k be a constant, F=F(x,y,z),G=G(x,y,z), and...Ch. 15.1 - Rewrite the identities in Exercises 31, 33, 35,...Ch. 15.1 - Rewrite the identities in Exercises 32, 34, 36,...Ch. 15.1 - Verify that the radius vector r=xi+yj+zk has the...Ch. 15.1 - Verify that the radius vector r=xi+yj+zk has the...Ch. 15.1 - Letr=xi+yj+zk,letr=r,letf be a differentiable...Ch. 15.1 - (a) Use part (a) of Exercise 43, Exercise 36, and...Ch. 15.1 - Use the result in Exercise 43(b) to show that the...Ch. 15.1 - Use the result of Exercise 43(b) to show that if F...Ch. 15.1 - A curve C is called a flow line of a vector field...Ch. 15.1 - Find a differential equation satisfied by the flow...Ch. 15.1 - Find a differential equation satisfied by the flow...Ch. 15.1 - Find a differential equation satisfied by the flow...Ch. 15.2 - The area of the surface extending upward from the...Ch. 15.2 - Suppose that a wire has equation y=1x(0x1) and...Ch. 15.2 - If C is the curve represented by the equations...Ch. 15.2 - Prob. 4QCECh. 15.2 - Let C be the line segment from (0.0)to(0,1). In...Ch. 15.2 - Let C be the line segment from (0,2)to(0,4). ln...Ch. 15.2 - Evaluate CFdr by inspection for the force field...Ch. 15.2 - Evaluate CFdr by inspection for the force field...Ch. 15.2 - Use (30) to explain why the line integral in part...Ch. 15.2 - (a) Use (30) to explain why the line integral in...Ch. 15.2 - Evaluate CFdr along the line segment C from PtoQ....Ch. 15.2 - Evaluate CFdr along the line segment C from PtoQ....Ch. 15.2 - Evaluate CFdr along the line segment C from PtoQ....Ch. 15.2 - Evaluate CFdr along the line segment C from PtoQ....Ch. 15.2 - Let C be the curve represented by the equations...Ch. 15.2 - Let C be the curve represented by the equations...Ch. 15.2 - In each part, evaluate the integral...Ch. 15.2 - In each part, evaluate the integral Cydx+zdyxdz...Ch. 15.2 - Prob. 15ESCh. 15.2 - Determine whether the statement is true or false....Ch. 15.2 - Determine whether the statement is true or false....Ch. 15.2 - If a smooth oriented curve C in the xy-plane is a...Ch. 15.2 - Evaluate the line integral with respect to s along...Ch. 15.2 - Evaluate the line integral with respect to s along...Ch. 15.2 - Evaluate the line integral with respect to s along...Ch. 15.2 - Evaluate the line integral with respect to s along...Ch. 15.2 - Evaluate the line integral along the curve C....Ch. 15.2 - Evaluate the line integral along the curve C....Ch. 15.2 - Evaluate the line integral along the curve C....Ch. 15.2 - Evaluate the line integral along the curve C....Ch. 15.2 - Evaluate the line integral along the curve C....Ch. 15.2 - Evaluate the line integral along the curve C....Ch. 15.2 - Evaluate the line integral along the curve C....Ch. 15.2 - Evaluate the line integral along the curve C....Ch. 15.2 - Use a CAS to evaluate the line integrals along the...Ch. 15.2 - Use a CAS to evaluate the line integrals along the...Ch. 15.2 - Evaluate Cydxxdy along the curve C shown in the...Ch. 15.2 - Evaluate Cydxxdy along the curve C shown in the...Ch. 15.2 - Evaluate Cx2zdxyx2dy+3dz along the curve C shown...Ch. 15.2 - Evaluate Cx2zdxyx2dy+3dz along the curve C shown...Ch. 15.2 - Evaluate CFdr along the curve C....Ch. 15.2 - Evaluate CFdr along the curves C....Ch. 15.2 - Evaluate CFdr along the curves C....Ch. 15.2 - Prob. 40ESCh. 15.2 - Find the mass of a thin wire shaped in the form of...Ch. 15.2 - Find the mass of a thin wire shaped in the form of...Ch. 15.2 - Find the mass of a thin wire shaped in the form of...Ch. 15.2 - Find the mass of a thin wire shaped in the form of...Ch. 15.2 - Find the work done by the force field F on a...Ch. 15.2 - Find the work done by the force F on a particle...Ch. 15.2 - Find the work done by the force field F on a...Ch. 15.2 - Find the work done by the force field F on a...Ch. 15.2 - Find the work done by the force field...Ch. 15.2 - Find the work done by the force field...Ch. 15.2 - Use a line integral to find the area of the...Ch. 15.2 - Use a line integral to find the area of the...Ch. 15.2 - As illustrated in the accompanying figure, a...Ch. 15.2 - Evaluate the integral Cxdyydxx2+y2, where C is the...Ch. 15.2 - Suppose that a particle moves through the force...Ch. 15.2 - A farmer weighting 150 lb carries a sack of gain...Ch. 15.2 - Suppose that a curve C in the xy-plane is smoothly...Ch. 15.3 - If C is a piecewise smooth curve from...Ch. 15.3 - Prob. 2QCECh. 15.3 - A potential function for the vector field...Ch. 15.3 - If a, b. and c are nonzero real numbers such that...Ch. 15.3 - Determine whether F is a conservative vector...Ch. 15.3 - Determine whether F is a conservative vector...Ch. 15.3 - Determine whether F is a conservative vector...Ch. 15.3 - Determine whether F is a conservative vector...Ch. 15.3 - Determine whether F is a conservative vector...Ch. 15.3 - Determine whether F is a conservative vector...Ch. 15.3 - In each part, evaluate C2xy3dx+1+3x2y2dy over the...Ch. 15.3 - Prob. 8ESCh. 15.3 - Show that the integral is independent of the path,...Ch. 15.3 - Show that the integral is independent of the path,...Ch. 15.3 - Show that the integral is independent of the path,...Ch. 15.3 - Show that the integral is independent of the path,...Ch. 15.3 - Show that the integral is independent of the path,...Ch. 15.3 - Show that the integral is independent of the path,...Ch. 15.3 - Confirm that the force field F is conservative in...Ch. 15.3 - Confirm that the force field F is conservative in...Ch. 15.3 - Confirm that the force field F is conservative in...Ch. 15.3 - Confirm that the force field F is conservative in...Ch. 15.3 - Determine whether the statement is true or false....Ch. 15.3 - Determine whether the statement is true or false....Ch. 15.3 - Determine whether the statement is true or false....Ch. 15.3 - Prob. 22ESCh. 15.3 - Find the exact value of CFdr using any method....Ch. 15.3 - Find the exact value of CFdr using any method....Ch. 15.3 - Use the numerical integration capability of a CAS...Ch. 15.3 - Use the numerical integration capability of a CAS...Ch. 15.3 - Is the vector field conservative? Explain.Ch. 15.3 - Is the vector field conservative? Explain.Ch. 15.3 - Prove: If Fx,y,z=fx,y,zi+gx,y,zj+hx,y,zk is a...Ch. 15.3 - Use the result in Exercise 31 to show that the...Ch. 15.3 - Find a nonzero function h for which...Ch. 15.3 - (a) In Example 3 of Section 15.1 we showed that...Ch. 15.3 - Use the result in Exercise 34(b). In each part,...Ch. 15.3 - Use the result in Exercise 34(b). Let...Ch. 15.3 - Prove Theorem 15.3.1 if C is a piecewise smooth...Ch. 15.3 - Prove that (b) implies (c) in Theorem 15.3.2.Ch. 15.3 - Complete the proof of Theorem 15.3.2 by showing...Ch. 15.4 - If C is the square with vertices 1,1 oriented...Ch. 15.4 - If C is the triangle with vertices 0,0,1,0,and1,1...Ch. 15.4 - Prob. 3QCECh. 15.4 - What region R and choice of functions fx,yandgx,y...Ch. 15.4 - Evaluate the line integral using Green’s Theorem...Ch. 15.4 - Prob. 2ESCh. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Use Green’s Theorem to evaluate the integral. In...Ch. 15.4 - Let C be the boundary of the region enclosed...Ch. 15.4 - Determine whether the statement is true or false....Ch. 15.4 - Determine whether the statement is true or false....Ch. 15.4 - Determine whether the statement is true or false....Ch. 15.4 - Determine whether the statement is true or false....Ch. 15.4 - Use a CAS to check Green’s Theorem by evaluating...Ch. 15.4 - In Example 3, we used Green’s Theorem to obtain...Ch. 15.4 - Use a line integral to find the area of the region...Ch. 15.4 - Use a line integral to find the area of the...Ch. 15.4 - Use the formula A=12Cydx+xdy to find the area of...Ch. 15.4 - Use the formula A=12Cydx+xdy to find the area of...Ch. 15.4 - Suppose that Fx,y=fx,yi+gx,yj is a vector field...Ch. 15.4 - Suppose that Fx,y,=fx,yi+gx,yj is a vector field...Ch. 15.4 - Prob. 27ESCh. 15.4 - In the accompanying figure, C is a smooth oriented...Ch. 15.4 - Use Green’s Theorem to find the work done by the...Ch. 15.4 - Use Green’s Theorem to find the work done by the...Ch. 15.4 - Evaluate Cydxxdy, where C is cardioid r=a1+cos02Ch. 15.4 - Let R be a plane region with area A whose boundary...Ch. 15.4 - Use the result in Exercise 32 to find the centroid...Ch. 15.4 - Use the result in Exercise 32 to find the centroid...Ch. 15.4 - Use the result in Exercise 32 to find the centroid...Ch. 15.4 - Use the result in Exercise 32 to find the centroid...Ch. 15.4 - Find a simple closed curve C with counterclockwise...Ch. 15.4 - (a) Let C be the line segment from a point a,b to...Ch. 15.4 - Evaluate the integral CFdr, where C is the...Ch. 15.4 - Evaluate the integral CFdr, where C is the...Ch. 15.4 - Discuss the role of the Fundamental Theorem of...Ch. 15.5 - Consider the surface integral fx,y,zdS. (a) If is...Ch. 15.5 - If is the triangular region with vertices...Ch. 15.5 - If is the sphere of radius 2 centered at the...Ch. 15.5 - If fx,y,z is the mass density function of a curved...Ch. 15.5 - Evaluate the surface integral fx,y,zdS fx,y,z=x2;...Ch. 15.5 - Evaluate the surface integral fx,y,zdS fx,y,z=xy;...Ch. 15.5 - Evaluate the surface integral fx,y,zdS fx,y,z=x2y;...Ch. 15.5 - Evaluate the surface integral fx,y,zdS...Ch. 15.5 - Evaluate the surface integral fx,y,zdS fx,y,z=xyz;...Ch. 15.5 - Evaluate the surface integral fx,y,zdS fx,y,z=x+y;...Ch. 15.5 - Evaluate the surface integral fx,y,zdS...Ch. 15.5 - Evaluate the surface integral fx,y,zdS...Ch. 15.5 - Determine whether the statement is true or false....Ch. 15.5 - Determine whether the statement is true or false....Ch. 15.5 - Determine whether the statement is true or false....Ch. 15.5 - Determine whether the statement is true or false....Ch. 15.5 - Sometimes evaluating a surface integral results in...Ch. 15.5 - Sometimes evaluating a surface integral results in...Ch. 15.5 - In some cases it is possible to use Definition...Ch. 15.5 - In some cases it is possible to use Definition...Ch. 15.5 - In some cases it is possible to use Definition...Ch. 15.5 - Set up, but do not evaluate, an iterated integral...Ch. 15.5 - Set up, but do not evaluate, an iterated integral...Ch. 15.5 - Use a CAS to confirm that the three integrals you...Ch. 15.5 - Try to confirm with a CAS that the three integrals...Ch. 15.5 - Set up, but do not evaluate, two different...Ch. 15.5 - Set up, but do not evaluate, two different...Ch. 15.5 - Use a CAS to confirm that the two integrals you...Ch. 15.5 - Use a CAS to find the value of the surface...Ch. 15.5 - Find the mass of the lamina with constant density...Ch. 15.5 - Find the mass of the lamina with constant density...Ch. 15.5 - Find the mass of the lamina that is the portion of...Ch. 15.5 - Find the mass of the lamina that is the portion of...Ch. 15.5 - If a curved lamina has constant density 0, what...Ch. 15.5 - Show that if the density of the lamina x2+y2+z2=a2...Ch. 15.5 - The centroid of a surface is defined by...Ch. 15.5 - The centroid of a surface is defined by...Ch. 15.5 - Evaluate the integral fx,y,zdS over the surface ...Ch. 15.5 - Prob. 36ESCh. 15.5 - Prob. 37ESCh. 15.5 - Prob. 38ESCh. 15.5 - Use a CAS to approximate the mass of the curved...Ch. 15.5 - The surface shown in the accompanying figure on...Ch. 15.5 - Discuss the similarities and differences between...Ch. 15.6 - In these exercises, F(x,y,z) denotes a vector...Ch. 15.6 - In these exercises, F(x,y,z) denotes a vector...Ch. 15.6 - In these exercises, F(x,y,z) denotes a vector...Ch. 15.6 - In these exercises, F(x,y,z) denotes a vector...Ch. 15.6 - Suppose that the surface of the unit cube in the...Ch. 15.6 - Find the flux of the constant vector field...Ch. 15.6 - Find the flux of F(x,y,z)=xi through a square of...Ch. 15.6 - Find the flux of F(x,y,z)=(y+1)j through a square...Ch. 15.6 - Find the flux of Fx,y,z=xi+yj+z2+4k through a 23...Ch. 15.6 - Find the flux of F(x,y,z)=2i+3j through a disk of...Ch. 15.6 - Find the flux of F(x,y,z)=9j+8k through a disk of...Ch. 15.6 - Prob. 8ESCh. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across ....Ch. 15.6 - Find the flux of the vector field F across in the...Ch. 15.6 - Find the flux of the vector field F across in the...Ch. 15.6 - Find the flux of the vector field F across in the...Ch. 15.6 - Find the flux of the vector field F across in the...Ch. 15.6 - Let be the surface of the cube bounded by the...Ch. 15.6 - Let be the closed surface consisting of the...Ch. 15.6 - Determine whether the statement is true or false....Ch. 15.6 - Determine whether the statement is true or false....Ch. 15.6 - Determine whether the statement is true or false....Ch. 15.6 - Determine whether the statement is true or false....Ch. 15.6 - Find the flux of F across the surface by...Ch. 15.6 - Find the flux of F across the surface by...Ch. 15.6 - Let x,y,andz be measured in meters, and suppose...Ch. 15.6 - Let x,y,andz be measured in meters, and suppose...Ch. 15.6 - (a) Derive the analogs of Formulas (12) and (13)...Ch. 15.6 - (a) Derive the analogs of Formulas (12) and (13)...Ch. 15.6 - Let F=rkr,wherer=xi+yj+zkandkisaconstant. (Note...Ch. 15.6 - Let F(x,y,z)=a2xi+(y/a)j+az2k and let be the...Ch. 15.6 - Let F(x,y,z)=6a+1xi4ayj+a2zk and let be the...Ch. 15.6 - Discuss the similarities and differences between...Ch. 15.6 - Write a paragraph explaining the concept of flux...Ch. 15.7 - Let G be a solid whose surface is oriented outward...Ch. 15.7 - The outward flux of Fx,y,z=xi+yj+zk across any...Ch. 15.7 - If Fx,y,z is the velocity vector field for a...Ch. 15.7 - If F(r)=cr3r is an inverse-square field, and if ...Ch. 15.7 - Verify Formula (1) in the Divergence Theorem by...Ch. 15.7 - Verify Formula (1) in the Divergence Theorem by...Ch. 15.7 - Verify Formula (1) in the Divergence Theorem by...Ch. 15.7 - Verify Formula (1) in the Divergence Theorem by...Ch. 15.7 - Determine whether the statement is true or false....Ch. 15.7 - Determine whether the statement is true or false....Ch. 15.7 - Determine whether the statement is true or false....Ch. 15.7 - Determine whether the statement is true or false....Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Use the Divergence Theorem to find the flux of F...Ch. 15.7 - Prove that if r=xi+yj+zkand is the surface of a...Ch. 15.7 - Use the result in Exercise 20 to find the outward...Ch. 15.7 - Let Fx,y,z=ai+bj+ck be a constant vector field and...Ch. 15.7 - Find a vector field Fx,y,z that has (a) positive...Ch. 15.7 - Let Fx,y,z be a nonzero vector field in 3-space...Ch. 15.7 - Does the result in Exercise 25 remain true if the...Ch. 15.7 - Prove the identity, assuming that F, , and G...Ch. 15.7 - Prove the identity, assuming that F, , and G...Ch. 15.7 - Prove the identity, assuming that F, , and G...Ch. 15.7 - Prove the identity, assuming that F, , and G...Ch. 15.7 - Prove the identity, assuming that F, , and G...Ch. 15.7 - Use the Divergence Theorem to find all positive...Ch. 15.7 - Determine whether the vector field Fx,y,z is free...Ch. 15.7 - Determine whether the vector field Fx,y,z is free...Ch. 15.7 - Determine whether the vector field Fx,y,z is free...Ch. 15.7 - Determine whether the vector field Fx,y,z is free...Ch. 15.7 - Let be the surface of the solid G that is...Ch. 15.8 - Let be a piecewise smooth oriented surface that...Ch. 15.8 - We showed in Example 2 that the vector field...Ch. 15.8 - (a) If 1and2 are two oriented surface that have...Ch. 15.8 - For steady-state flow, the maximum circulation...Ch. 15.8 - Verify Formula (2) in stokes’ Theorem by...Ch. 15.8 - Verify Formula (2) in stokes’ Theorem by...Ch. 15.8 - Verify Formula (2) in stokes’ Theorem by...Ch. 15.8 - Verify Formula (2) in stokes’ Theorem by...Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Use Stokes’s Theorem to evaluate CF.dr....Ch. 15.8 - Determine whether the statement is true or false....Ch. 15.8 - Determine whether the statement is true or false....Ch. 15.8 - Determine whether the statement is true or false....Ch. 15.8 - Determine whether the statement is true or false....Ch. 15.8 - Consider the vector field given by the formula...Ch. 15.8 - (a) Let denote the surface of a solid G with n...Ch. 15.8 - The figures in these exercises show a horizontal...Ch. 15.8 - The figures in these exercises show a horizontal...Ch. 15.8 - Let F(x,y,z) be a conservation vector field in...Ch. 15.8 - In 1831 the physicist Michael Faraday discovered...Ch. 15.8 - Let be the portion of the paraboloid z=1x2y2 for...Ch. 15.8 - Discuss what it mean to say that the curl of a...Ch. 15.8 - Compare and contrast the Fundamental Theorem of...Ch. 15 - In words, what is a vector field? Give some...Ch. 15 - (a) Give a physical example of an inverse-square...Ch. 15 - Find an explicit coordinate expression for the...Ch. 15 - Find x+yxy.Ch. 15 - Find curl zi+xj+yk.Ch. 15 - Let Fx,y,z=xx2+y2i+yx2+y2j+zx2+y2k Sketch the...Ch. 15 - Assume that C is the parametric curve x=xt,y=yt,...Ch. 15 - (a) Express the mass M of a thin wire in 3-space...Ch. 15 - Give a physical interpretation of CFTds.Ch. 15 - State some alternative notations for CFTds.Ch. 15 - Evaluate the line integral. Cxyds;C:x2+y2=1Ch. 15 - Evaluate the line integral....Ch. 15 - Evaluate the line integral....Ch. 15 - Find the work done by the force field Fx,y=y2i+xyj...Ch. 15 - State the Fundamental Theorem of Line Integrals,...Ch. 15 - Evaluate Cfdr where fx,y,z=xy2z3 and...Ch. 15 - Let Fx,y=yi2xj. (a) Find a nonzero function hx...Ch. 15 - Let Fx,y=yexy1i+xexyj. (a) Show that F is a...Ch. 15 - State Green's Theorem, including all of the...Ch. 15 - Express the area of a plane region as a line...Ch. 15 - Let and denote angles that satisfy 02 and assume...Ch. 15 - (a) Use Green's Theorem to prove that Cfxdx+gydy=0...Ch. 15 - Assume that is the parametric surface...Ch. 15 - Evaluate zdS;:x2+y2=10z1.Ch. 15 - Do you think that the surface in the accompanying...Ch. 15 - Give a physical interpretation of FndS.Ch. 15 - Find the flux of Fx,y,z=xi+yj+2zk through the...Ch. 15 - Find the flux of Fx,y,z=xi+2yj+3zk through the...Ch. 15 - State the Divergence Theorem and Stokes' Theorem,...Ch. 15 - Let G be a solid with the surface oriented by...Ch. 15 - Let be the sphere x2+y2+z2=1, let n be an inward...Ch. 15 - Use Stokes' Theorem to evaluate curlFndS where...Ch. 15 - Prob. 33RECh. 15 - With the aid of Exercise 33, determine whether F...Ch. 15 - With the aid of Exercise 33, determine whether F...Ch. 15 - As discussed in Example 1 of Section 15.1,...
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- ٣/١ B msl kd 180 Ka, Sin (1) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW Rotor input 5 0.05 : loo kw 6) 1 /0001 ined sove in peaper I need a detailed solution on paper please وه اذا ميريد شرح الكتب فقط ١٥٠ DC 7) rotor a ' (y+xlny + xe*)dx + (xsiny + xlnx + dy = 0. Q1// Find the solution of: ( 357arrow_forward۳/۱ R₂ = X2 2) slots per pole per phase 3/31 B. 180 msl Kas Sin (I) 1sin() sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30): 0.866 4) Rotating 5) Synchronous speeds 120×50 looo G 1000-950 1000 Copper losses 5kw Rotor input 5 loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط look 7) rotor DC ined sove in peaper I need a detailed solution on paper please 0 64 Find the general solution of the following equations: QI//y(4)-16y= 0. Find the general solution of the following equations: Q2ll yll-4y/ +13y=esinx.arrow_forwardR₂ = X2 2) slots per pole per phase = 3/31 B-180 60 msl kd Kas Sin () 2 I sin (6) sin(30) Sin (30) اذا مريد شرح الكتب بس 0 بالفراغ 3 Cos (30) 0.866 4) Rotating ined sove in peaper 5) Synchronous speed s 120×50 6 s = 1000-950 1000 Copper losses 5kw Rotor input 5 0.05 6) 1 loo kw اذا ميريد شرح الكتب فقط Look 7) rotov DC I need a detailed solution on paper please 0 64 Solve the following equations: 0 Q1// Find the solution of: ( y • with y(0) = 1. dx x²+y²arrow_forward
- R₂ = X2 2) slots per pole per phase = 3/3 1 B-180-60 msl Ka Sin (1) Isin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 s = 1000-950 1000 Copper losses 5kw Rotor input 5 6) 1 0.05 G 50105 loo kw اذا ميريد شرح الكتب فقط look 7) rotov DC ined sove in peaper I need a detailed solution on paper please 064 2- A hot ball (D=15 cm ) is cooled by forced air T.-30°C, the rate of heat transfer from the ball is 460.86 W. Take for the air -0.025 Wim °C and Nu=144.89, find the ball surface temperature a) 300 °C 16 b) 327 °C c) 376 °C d) None か = 750 01arrow_forwardDon't do 14. Please solve 19arrow_forwardPlease solve 14 and 15arrow_forward
- 1. Consider the following system of equations: x13x2 + 4x3 - 5x4 = 7 -2x13x2 + x3 - 6x4 = 7 x16x213x3 - 21x4 = 28 a) Solve the system. Write your solution in parametric and vector form. b) What is a geometric description of the solution. 7 c) Is v = 7 in the span of the set S= [28. 1 HE 3 -5 3 ·6 ? If it is, write v 6 as a linear combination of the vectors in S. Justify. d) How many solutions are there to the associated homogeneous system for the system above? Justify. e) Let A be the coefficient matrix from the system above. Find the set of all solutions to Ax = 0. f) Is there a solution to Ax=b for all b in R³? Justify.arrow_forward4. Suppose that A is made up of 5 column vectors in R³, and suppose that the rank(A)=3. a. How many solutions are there to Ax=0? Justify. b. What is a geometric description for the nullspace(A)? Justify. c. Do the column vectors of A span R³? Justify. d. Is A invertible? Justify.arrow_forward3. Suppose that A is 5 x 5 and rank(A)=4. Use this information to answer the following. a. Give a geometric description of nullspace(A). Justify. b. Is A invertible? Justify. c. Give a geometric description of the span of the column vectors of A. What space are the column vectors of A in? Justify. d. What is determinant of A? Justify.arrow_forward
- 2. Consider the matrix: A || 1 1 -3 14 2 1 01 4 1 2 2 -26 1 -3 1 5] a) What is rank(A)? b) Is A invertible? Justify. c) Find the nullspace(A). Justify. d) Is the trivial solution the only solution to Ax=0? Justify. e) What is the span of the column vectors of A? Justify.arrow_forwardE 5. Suppose that S={v € R²: v = [2x² - 3]}. Is S a subspace of R²? Prove or disprovearrow_forward6. Suppose that V1, V2 ER", show that span{v1, v2} is a subspace of Rn.arrow_forward
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