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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781285740621

Chapter 16.R, Problem 33E

Textbook Problem

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Use Stokes’ Theorem to evaluate
*C* is the triangle with vertices

To determine

**To evaluate:**

**1) Concept:**

i) Stokes’ Theorem:

Let

ii)

If

iii) If

Where

iv) If

**2) Given:**

**3) Calculation:**

The given vector field is,

The boundary curve

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Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...Ch. 16.1 - Sketch the vector field F by drawing a diagram...Ch. 16.1 - Sketch the vector field F by drawing a diagram...Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...Ch. 16.1 - 110 Sketch the vector field F by drawing a diagram...

Ch. 16.1 - Match the vector fields F with the plots labelled...Ch. 16.1 - Match the vector fields F with the plots labelled...Ch. 16.1 - Match the vector fields F with the plots labelled...Ch. 16.1 - Match the vector fields F with the plots labeled...Ch. 16.1 - Match the vector fields F on 3 with the plots...Ch. 16.1 - Match the vector fields F on 3 with the plots...Ch. 16.1 - Match the vector fields F on 3 with the plots...Ch. 16.1 - Match the vector fields F on 3 with the plots...Ch. 16.1 - If you have a CAS that plots vector fields the...Ch. 16.1 - Let F(x)=(r22r)x, where x=x,y and r=|x|. Use a CAS...Ch. 16.1 - Find the gradient vector field of f....Ch. 16.1 - Find the gradient vector field of f. f(s,t)=2s+3tCh. 16.1 - Find the gradient vector field of f....Ch. 16.1 - Find the gradient vector field of f....Ch. 16.1 - Find the gradient vector field f of f and sketch...Ch. 16.1 - Find the gradient vector field f of f and sketch...Ch. 16.1 - Plot the gradient vector field of f together with...Ch. 16.1 - Plot the gradient vector field of f together with...Ch. 16.1 - Match the functions f with the plots of their...Ch. 16.1 - Match the functions f with the plots of their...Ch. 16.1 - Match the functions f with the plots of their...Ch. 16.1 - Match the functions f with the plots of their...Ch. 16.1 - A particle moves in a velocity field...Ch. 16.1 - At time t=1, a particle is located at position...Ch. 16.1 - The flow lines or streamlines of a vector field...Ch. 16.1 - a Sketch the vector field F(x,y)=i+xj and then...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Evaluate the line integral, where C is the given...Ch. 16.2 - Let F be the vector fields shown in the figure. a...Ch. 16.2 - The figure shows a vector field F and two curves...Ch. 16.2 - Evaluate the line integral cFdr, where C is given...Ch. 16.2 - Evaluate the line integral CFdr, where C is given...Ch. 16.2 - Evaluate the line integral CFdr, where C is given...Ch. 16.2 - Evaluate the line integral CFdr, where C is given...Ch. 16.2 - Use a calculator to evaluate the line integral...Ch. 16.2 - Use a calculator to evaluate the line integral...Ch. 16.2 - Use a calculator to evaluate the line integral...Ch. 16.2 - Use a calculator to evaluate the line integral...Ch. 16.2 - Use a graph of the vector field F and the curve C...Ch. 16.2 - Use a graph of the vector field F and the curve C...Ch. 16.2 - a Evaluate the line integral CFdr, where...Ch. 16.2 - a Evaluate the line integral CFdr, where...Ch. 16.2 - Find the exact value of Cx3y3zds, where C is the...Ch. 16.2 - a Find the work done by the force field...Ch. 16.2 - A thin wire is bent into the shape of a semicircle...Ch. 16.2 - A thin wire has the shape of the first-quadrant...Ch. 16.2 - a Write the formulas similar to Equations 4 for...Ch. 16.2 - Find the mass and center of mass of a wire in the...Ch. 16.2 - If a wire with linear density p(x,y) lies along a...Ch. 16.2 - If a wire with linear density p(x,y,z) lies along...Ch. 16.2 - Find the work done by the force field...Ch. 16.2 - Find the work done by the force field...Ch. 16.2 - Find the work done by the force field...Ch. 16.2 - The force exerted by an electric charge at the...Ch. 16.2 - The position of an object with mass m at time t is...Ch. 16.2 - An object with mass m moves with position function...Ch. 16.2 - A 160-lb man carries a 25-lb can of paint up a...Ch. 16.2 - Suppose there is a hole in the can of paint in...Ch. 16.2 - a Show that a constant force field does zero work...Ch. 16.2 - The base of a circular fence with radius 10 m is...Ch. 16.2 - If C is a smooth curve given by a vector function...Ch. 16.2 - If C is a smooth curve given by a vector function...Ch. 16.2 - An object moves along the curve C shown in the...Ch. 16.2 - Experiments show that a steady current I in a long...Ch. 16.3 - The figure shows a curve C and a contour map of a...Ch. 16.3 - A table of values of a function f with continuous...Ch. 16.3 - Determine whether or not F is a conservative...Ch. 16.3 - Determine whether or not F is a conservative...Ch. 16.3 - Determine whether or not F is a conservative...Ch. 16.3 - Determine whether or not F is a conservative...Ch. 16.3 - Determine whether or not F is a conservative...Ch. 16.3 - Determine whether or not F is a conservative...Ch. 16.3 - Determine whether or not F is a conservative...Ch. 16.3 - Determine whether or not F is a conservative...Ch. 16.3 - The figure shows the vector field F(x,y)=2xy,x2...Ch. 16.3 - a Find a function f such that F=f and b use part a...Ch. 16.3 - a Find a function f such that F=f and b use part a...Ch. 16.3 - a Find a function f such that F=f and b use part a...Ch. 16.3 - a Find a function f such that F=f and b use part a...Ch. 16.3 - a Find a function f such that F=f and b use part a...Ch. 16.3 - a Find a function f such that F=f and b use part a...Ch. 16.3 - a Find a function f such that F=f and b use part a...Ch. 16.3 - Show that the line integral is independent of path...Ch. 16.3 - Show that the line integral is independent of path...Ch. 16.3 - Suppose youre asked to determine the curve that...Ch. 16.3 - Suppose an experiment determines that the amount...Ch. 16.3 - Find the work done by the force field F in moving...Ch. 16.3 - Find the work done by the force field F in moving...Ch. 16.3 - Is the vector field shown in the figure...Ch. 16.3 - Is the vector field shown in the figure...Ch. 16.3 - If F(x,y)=sinyi+(1+xcosy)j, use a plot to guess...Ch. 16.3 - Let F=f, where f(x,y)=sin(x2y). Find curves C1 and...Ch. 16.3 - Show that if the vector field F=Pi+Qj+Rk is...Ch. 16.3 - Use Exercise 29 to show that the line integral...Ch. 16.3 - Determine whether or not the given set is a open,...Ch. 16.3 - Determine whether or not the given set is a open,...Ch. 16.3 - Determine whether or not the given set is a open,...Ch. 16.3 - Determine whether or not the given set is a open,...Ch. 16.3 - Let F(x,y)=yi+xjx2+y2. a Show that P/y=Q/x. b Show...Ch. 16.3 - a Suppose that F is an inverse square force field,...Ch. 16.4 - Evaluate the line integral by two methods: a...Ch. 16.4 - Evaluate the line integral by two methods: a...Ch. 16.4 - Evaluate the line integral by two methods: a...Ch. 16.4 - Evaluate the line integral by two methods: a...Ch. 16.4 - Use Greens Theorem to evaluate the line integral...Ch. 16.4 - Use Greens Theorem to evaluate the line integral...Ch. 16.4 - Use Greens Theorem to evaluate the line integral...Ch. 16.4 - Use Greens Theorem to evaluate the line integral...Ch. 16.4 - Use Greens Theorem to evaluate the line integral...Ch. 16.4 - Use Greens Theorem to evaluate the line integral...Ch. 16.4 - Use Greens Theorem to evaluate cFdr. Check the...Ch. 16.4 - Use Greens Theorem to evaluate cFdr. Check the...Ch. 16.4 - Use Greens Theorem to evaluate cFdr. Check the...Ch. 16.4 - Use Greens Theorem to evaluate cFdr. Check the...Ch. 16.4 - Verify Greens Theorem by using a computer algebra...Ch. 16.4 - Verify Greens Theorem by using a computer algebra...Ch. 16.4 - Use Greens Theorem to find the work done by the...Ch. 16.4 - A particle starts at the origin, moves along the...Ch. 16.4 - Use one of the formulas in 5 to find the area...Ch. 16.4 - If a circle C with radius 1 rolls along the...Ch. 16.4 - a If C is the fine segment connecting the point...Ch. 16.4 - Let D be a region bounded by a simple closed path...Ch. 16.4 - Use Exercise 22 to find the centroid of a...Ch. 16.4 - Use Exercise 22 to find the centroid of the...Ch. 16.4 - A plane lamina with constant density (x,y)=...Ch. 16.4 - Use Exercise 25 to find the moment of inertia of a...Ch. 16.4 - Use the method of Example 5 to calculate CFdr,...Ch. 16.4 - Calculate CFdr, where F(x,y)=x2+y,3xy2 and C is...Ch. 16.4 - If F is the vector field of Example 5, show that...Ch. 16.4 - Complete the proof of the special case of Greens...Ch. 16.4 - Use Greens Theorem to prove the change of...Ch. 16.5 - Find a the curl and b the divergence of the vector...Ch. 16.5 - Find a the curl and b the divergence of the vector...Ch. 16.5 - Find a the curl and b the divergence of the vector...Ch. 16.5 - Find a the curl and b the divergence of the vector...Ch. 16.5 - Find a the curl and b the divergence of the vector...Ch. 16.5 - Find a the curl and b the divergence of the vector...Ch. 16.5 - Find a the curl and b the divergence of the vector...Ch. 16.5 - Find a the curl and b the divergence of the vector...Ch. 16.5 - The vector field F is shown in the xy-plane and...Ch. 16.5 - The vector field F is shown in the xy-plane and...Ch. 16.5 - The vector field F is shown in the xy-plane and...Ch. 16.5 - Let f be a scalar field and F a vector field....Ch. 16.5 - Determine whether or not the vector field is...Ch. 16.5 - Determine whether or not the vector field is...Ch. 16.5 - Determine whether or not the vector field is...Ch. 16.5 - Determine whether or not the vector field is...Ch. 16.5 - Determine whether or not the vector field is...Ch. 16.5 - Determine whether or not the vector field is...Ch. 16.5 - Is there a vector field G on 3 such that curl...Ch. 16.5 - Is there a vector field G on 3 such that curl...Ch. 16.5 - Show that any vector field of the form...Ch. 16.5 - Show that any vector field of the form...Ch. 16.5 - Prove the identity, assuming that the appropriate...Ch. 16.5 - Prove the identity, assuming that the appropriate...Ch. 16.5 - Prove the identity, assuming that the appropriate...Ch. 16.5 - Prove the identity, assuming that the appropriate...Ch. 16.5 - Prove the identity, assuming that the appropriate...Ch. 16.5 - Prove the identity, assuming that the appropriate...Ch. 16.5 - Prove the identity, assuming that the appropriate...Ch. 16.5 - Let r=xi+yj+zk and r=|r|. Verify each identity. a...Ch. 16.5 - Let r=xi+yj+zk and r=|r|. Verify each identity. a...Ch. 16.5 - Let r=xi+yj+zk and r=|r|. If F=r/rp, find div F....Ch. 16.5 - Use Greens Theorem in the form of Equation 13 to...Ch. 16.5 - Use Greens first identity Exercise 33 to prove...Ch. 16.5 - Recall from Section 14.3 that a function g is...Ch. 16.5 - Use Greens first identity to show that if f is...Ch. 16.5 - This exercise demonstrates a connection between...Ch. 16.5 - Maxwells equations relating the electric field E...Ch. 16.5 - We have seen that all vector fields of the form...Ch. 16.6 - Determine whether the points P and Q lie on the...Ch. 16.6 - Determine whether the points P and Q lie on the...Ch. 16.6 - Identify the surface with the given vector...Ch. 16.6 - Identify the surface with the given vector...Ch. 16.6 - Identify the surface with the given vector...Ch. 16.6 - Identify the surface with the given vector...Ch. 16.6 - Use a computer to graph the parametric surface....Ch. 16.6 - Use a computer to graph the parametric surface....Ch. 16.6 - Use a computer to graph the parametric surface....Ch. 16.6 - Use a computer to graph the parametric surface....Ch. 16.6 - Use a computer to graph the parametric surface....Ch. 16.6 - Use a computer to graph the parametric surface....Ch. 16.6 - Match the equations with the graphs labeled IVI...Ch. 16.6 - Match the equations with the graphs labeled IVI...Ch. 16.6 - Match the equations with the graphs labeled IVI...Ch. 16.6 - Match the equations with the graphs labeled IVI...Ch. 16.6 - Match the equations with the graphs labeled IVI...Ch. 16.6 - Match the equations with the graphs labeled IVI...Ch. 16.6 - Find da parametric representation for the surface....Ch. 16.6 - Find da parametric representation for the surface....Ch. 16.6 - Find da parametric representation for the surface....Ch. 16.6 - Find da parametric representation for the surface....Ch. 16.6 - Find da parametric representation for the surface....Ch. 16.6 - Find da parametric representation for the surface....Ch. 16.6 - Find da parametric representation for the surface....Ch. 16.6 - Find da parametric representation for the surface....Ch. 16.6 - Use a graphing device to produce a graph that...Ch. 16.6 - Use a graphing device to produce a graph that...Ch. 16.6 - Find parametric equations for the surface obtained...Ch. 16.6 - Find parametric equations for the surface obtained...Ch. 16.6 - a What happens to the spiral tube in Example 2 see...Ch. 16.6 - The surface with parametric equations...Ch. 16.6 - Find an equation of the tangent plane to the given...Ch. 16.6 - Find an equation of the tangent plane to the given...Ch. 16.6 - Find an equation of the tangent plane to the given...Ch. 16.6 - Find an equation of the tangent plane to the given...Ch. 16.6 - Find an equation of the tangent plane to the given...Ch. 16.6 - Find an equation of the tangent plane to the given...Ch. 16.6 - Find the area of the surface. The part of the...Ch. 16.6 - Find the area of the surface. The part of the...Ch. 16.6 - Find the area of the surface. The part of the...Ch. 16.6 - Find the area of the surface. The part of the cone...Ch. 16.6 - Find the area of the surface. The surface...Ch. 16.6 - Find the area of the surface. The part of the...Ch. 16.6 - Find the area of the surface. The part of the...Ch. 16.6 - Find the area of the surface. The part of the...Ch. 16.6 - Find the area of the surface. The part of the...Ch. 16.6 - Find the area of the surface. The helicoid or...Ch. 16.6 - Find the area of the surface. The surface with...Ch. 16.6 - Find the area of the surface. The part of the...Ch. 16.6 - If the equation of a surface S is z=f(x,y), where...Ch. 16.6 - Find the area of the surface correct to four...Ch. 16.6 - Find the area of the surface correct to four...Ch. 16.6 - Find, to four decimal places, the area of the part...Ch. 16.6 - a Use the Midpoint Rule for double integrals see...Ch. 16.6 - Find the area of the surface with vector equation...Ch. 16.6 - Find the exact area of the surface...Ch. 16.6 - a Set up, but do not evaluate, a double integral...Ch. 16.6 - a Show that the parametric equations...Ch. 16.6 - a Show that the parametric equations...Ch. 16.6 - Find the area of the part of the sphere...Ch. 16.6 - The figure shows the surface created when the...Ch. 16.6 - Find the area of the part of the sphere...Ch. 16.6 - a Find a parametric representation for the torus...Ch. 16.7 - Let S be the surface of the box enclosed by the...Ch. 16.7 - A surface S consists of the cylinder x2+y2=1,1z1,...Ch. 16.7 - Let H be the hemisphere x2+y2+z2=50,z0, and...Ch. 16.7 - Suppose that f(x,y,z)=g(x2+y2+z2), where g is a...Ch. 16.7 - Evaluate the surface integral. S(x+y+z)dS, S is...Ch. 16.7 - Evaluate the surface integral. SxyzdS, S is the...Ch. 16.7 - Evaluate the surface integral....Ch. 16.7 - Evaluate the surface integral. S(x2+y2)dS, S is...Ch. 16.7 - Evaluate the surface integral. Sx2yzdS, S is the...Ch. 16.7 - Evaluate the surface integral. SxzdS, S is the...Ch. 16.7 - Evaluate the surface integral. SxdS, S is the...Ch. 16.7 - Evaluate the surface integral. SydS, S is the...Ch. 16.7 - Evaluate the surface integral. Sz2dS, S is the...Ch. 16.7 - Evaluate the surface integral. Sy2z2dS, S is the...Ch. 16.7 - Evaluate the surface integral. SxdS, S is the...Ch. 16.7 - Evaluate the surface integral. Sy2dS, S is the...Ch. 16.7 - Evaluate the surface integral. S(x2z+y2z)dS, S is...Ch. 16.7 - Evaluate the surface integral. S(x+y+z)dS, S is...Ch. 16.7 - Evaluate the surface integral. SxzdS, S is the...Ch. 16.7 - Evaluate the surface integral. S(x2+y2+z2)dS S is...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate the surface integral SFdS for the given...Ch. 16.7 - Evaluate S(x2+y2+z2)dS correct to four decimal...Ch. 16.7 - Find the exact value of SxyzdS, where S is the...Ch. 16.7 - Find the value of Sx2y2z2dS correct to four...Ch. 16.7 - Find the flux of F(x,y,z)=sin(xyz)i+x2yj+z2ex/5k...Ch. 16.7 - Find a formula for SFdS similar to Formula 10 for...Ch. 16.7 - Find a formula for SFdS similar to Formula 10 for...Ch. 16.7 - Find the centre of mass of the hemisphere...Ch. 16.7 - Find the mass of a thin funnel in the shape of a...Ch. 16.7 - a Give an integral expression for the moment of...Ch. 16.7 - Let S be the part of the sphere x2+y2+z2=25 that...Ch. 16.7 - A fluid has density 870 kg/m3 and flows with...Ch. 16.7 - Seawater has density 1025 kg/m3 and flows in a...Ch. 16.7 - Use Gausss Law to find the charge contained in the...Ch. 16.7 - Use Gausss Law to find the charge enclosed by the...Ch. 16.7 - The temperature at the point (x,y,z) in a...Ch. 16.7 - The temperature at a point in a ball with...Ch. 16.7 - Let F be an inverse square field, that is,...Ch. 16.8 - A hemisphere H and a portion P of a paraboloid are...Ch. 16.8 - Use Stokes Theorem to evaluate ScurlFdS...Ch. 16.8 - Use Stokes Theorem to evaluate ScurlFdS....Ch. 16.8 - Use Stokes Theorem to evaluate ScurlFdS....Ch. 16.8 - Use Stokes Theorem to evaluate ScurlFdS....Ch. 16.8 - Use Stokes Theorem to evaluate ScurlFdS...Ch. 16.8 - Use Stokes Theorem to evaluate cFdr. In each case...Ch. 16.8 - Use Stokes Theorem to evaluate cFdr. In each case...Ch. 16.8 - Use Stokes Theorem to evaluate cFdr. In each case...Ch. 16.8 - Use Stokes Theorem to evaluate cFdr. In each case...Ch. 16.8 - a Use Stokes Theorem to evaluate cFdr, where...Ch. 16.8 - a Use Stokes Theorem to evaluate cFdr, where...Ch. 16.8 - Verify the Stokes Theorem is true for the given...Ch. 16.8 - Verify that Stokes Theorem is true for given...Ch. 16.8 - Verify that Stokes Theorem is true for given...Ch. 16.8 - Let C be a simple closed smooth curve that lies in...Ch. 16.8 - A particle moves along line segments from the...Ch. 16.8 - Evaluate C(y+sinx)dx+(z2+cosy)dy+x3dz where C is...Ch. 16.8 - If S is a sphere and F satisfies the hypotheses of...Ch. 16.8 - Suppose S and C satisfy the hypotheses of Stokes...Ch. 16.9 - Verify that the Divergence Theorem is true for the...Ch. 16.9 - Verify that the Divergence Theorem is true for the...Ch. 16.9 - Verify that the Divergence Theorem is true for the...Ch. 16.9 - Verify that the Divergence Theorem is true for the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use a computer algebra system to plot the vector...Ch. 16.9 - Use a Divergence Theorem to evaluate SFdS, where...Ch. 16.9 - Let F(x,y,z)=ztan1(y2)i+z3ln(x2+1)j+zk. Find the...Ch. 16.9 - A vector field F is shown. Use the interpretation...Ch. 16.9 - a Are the points P1 and P2 sources or sinks for...Ch. 16.9 - Plot the vector field and guess where div F0 and...Ch. 16.9 - Plot the vector field and guess where div F0 and...Ch. 16.9 - Verify that div E=0 for the electric field...Ch. 16.9 - Use the Divergence Theorem to evaluate...Ch. 16.9 - Prove each identity, assuming that S and E satisfy...Ch. 16.9 - Prove each identity, assuming that S and E satisfy...Ch. 16.9 - Prove each identity, assuming that S and E satisfy...Ch. 16.9 - Prove each identity, assuming that S and E satisfy...Ch. 16.9 - Prove each identity, assuming that S and E satisfy...Ch. 16.9 - Prove each identity, assuming that S and E satisfy...Ch. 16.9 - Suppose S and E satisfy the conditions of the...Ch. 16.9 - A solid occupies a region E with surface S and is...Ch. 16.R - What is a vector field? Give three examples that...Ch. 16.R - a What is a conservative vector field? b What is...Ch. 16.R - a Write the definition of the line integral of a...Ch. 16.R - a Define the line integral of a vector field F...Ch. 16.R - State the fundamental Theorem for line integrals.Ch. 16.R - a What does it mean to say that cF.dr is...Ch. 16.R - State Greens Theorem.Ch. 16.R - Write expressions for the area enclosed by a curve...Ch. 16.R - Suppose F is a vector field on 3 a Define curl F....Ch. 16.R - If F = P i Q b, how do you determine whether F is...Ch. 16.R - a What is a parametric surface? What are its grid...Ch. 16.R - a Write the definition of the surface integral of...Ch. 16.R - a What is an oriented surface? Give an example of...Ch. 16.R - State Stokes Theorem.Ch. 16.R - State Divergence Theorem.Ch. 16.R - In what ways are the Fundamental Theorem for Line...Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - Determine whether the statement is true or false....Ch. 16.R - A vector field F, a curve C, and a point P are...Ch. 16.R - Evaluate the line integral. cxds, C is the arc of...Ch. 16.R - Evaluate the line integral. cyzcosxds,...Ch. 16.R - Evaluate the line integral. cydx+(x+y2)dy, C is...Ch. 16.R - Evaluate the line integral. cy3dx+x2dy, C is the...Ch. 16.R - Evaluate the line integral. cxydx+eydy+xzdz, C is...Ch. 16.R - Evaluate the line integral. cxydx+y2dy+yzdz, C is...Ch. 16.R - Evaluate the line integral. cFdr, where...Ch. 16.R - Evaluate the line integral. cFdr, where...Ch. 16.R - Find the work done by the force field...Ch. 16.R - Show that F is a conservative vector field. Then...Ch. 16.R - Show that F is a conservative vector field. Then...Ch. 16.R - Show that F is a conservative and use this fact to...Ch. 16.R - Show that F is a conservative and use this fact to...Ch. 16.R - Verify that Greens Theorem is true for the line...Ch. 16.R - Use Greens Theorem to evaluate c1+x3dx+2xydy where...Ch. 16.R - Use Greens theorem to evaluate cx2ydxxy2dy, where...Ch. 16.R - Find curl F and div F if...Ch. 16.R - Show that there is no vector field G such that...Ch. 16.R - If F and G are vector fields whose component...Ch. 16.R - If C is any piecewise-smooth simple closed plane...Ch. 16.R - If f and g are twice differentiable functions,...Ch. 16.R - If f is a harmonic function, that is, 2f=0, show...Ch. 16.R - a Sketch the curve C with parametric equations...Ch. 16.R - Find the area of the part of the surface z=x2+2y...Ch. 16.R - a Find an equation of the tangent plane at the...Ch. 16.R - Evaluate the surface integral. szdS, where S is...Ch. 16.R - Evaluate the surface integral. s(x2z+y2z)dS, where...Ch. 16.R - Evaluate the surface integral. sFdS, where...Ch. 16.R - Evaluate the surface integral. sFdS, where...Ch. 16.R - Verify that Stokes Theorem is true for the vector...Ch. 16.R - Use Stokes Theorem to evaluate scurlFdS, where...Ch. 16.R - Use Stokes Theorem to evaluate cFdr, where...Ch. 16.R - Use the Divergence Theorem to calculate the...Ch. 16.R - Verify that the Divergence Theorem is true for the...Ch. 16.R - Compute the outward flux of...Ch. 16.R - Let F(x,y,z)=(3x2yz3y)i+(x3z3x)j+(x3y+2z)k...Ch. 16.R - Let F(x,y)=(2x3+2xy22y)i+(2y3+2x2y+2x)jx2+y2...Ch. 16.R - Find sFndS, where F(x,y,z)=xi+yj+zk and S is the...Ch. 16.R - If the components of F have continuous second...Ch. 16.R - If a is a constant vector, r=xi+yj+zk, and S is an...Ch. 16.P - Let S be a smooth parametric surface and P be a...Ch. 16.P - Find the positively oriented simple closed curve C...Ch. 16.P - Let C be a simple closed piecewise-smooth space...Ch. 16.P - Investigate the shape of the surface with...Ch. 16.P - Prove the following identity:...Ch. 16.P - The depicts the sequence of events in each...

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Let a=log2,b=log3, and c=log7. In Exercises 2946, use the logarithm identities to express the given quantity in...

Finite Mathematics and Applied Calculus (MindTap Course List)

A model for the basal metabolism rate, in kcal/h, of a young man is R(t) = 85 0.18 cos(t/12), where t is the t...

Single Variable Calculus: Early Transcendentals, Volume I

What is the connection between vector functions and space curves?

Multivariable Calculus

In Exercises 15-18, find the limit (if it exists). limx0x+93x

Calculus: An Applied Approach (MindTap Course List)

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power serie...

Calculus: Early Transcendentals

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Precalculus: Mathematics for Calculus (Standalone Book)

SOC Are middle-class families more likely than working-class families to maintain contact with kin? Write a par...

Essentials Of Statistics

In a distribution with positive skew, where are the scoreswith the highest frequencies located? a. On the right...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). 4. limx1(x43x)(x2+5x+3)

Single Variable Calculus

Let g be the function defined by g(u) = (3u 2)3/2. Find g(1), g(6), g(113), and g(u + 1).

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Convert the expressions in Exercises 8596 radical form. (x1/2y1/3)1/5

Finite Mathematics

For Problems 9-19. please provide the following information. (a) What is the level of significance? State the n...

Understanding Basic Statistics

A psychology class consists of 28 males and 52 females. If the professor selects names from the class list usin...

Statistics for The Behavioral Sciences (MindTap Course List)

Determine whether the argument is an example of inductive reasoning or deductive reasoning. We had rain each da...

Mathematical Excursions (MindTap Course List)

For Problems 5-54, perform the following operations with real numbers. Objectives 3-6 755

Intermediate Algebra

Let 1 0, 2 0, with 1 + 2 = . Then P(z1X-/nz2)=1- a. Use this equation to derive a more general expression for...

Probability and Statistics for Engineering and the Sciences

Find the area of each rectangle: b=36ft,h=18ft

Elementary Technical Mathematics

In Problems 33-38, simplify so that only positive exponents remain. Assume that all variables are positive. (x1...

Mathematical Applications for the Management, Life, and Social Sciences

Let f(x) = k (3x x2) if 0 x 3 and f(x) = 0 if x 0 or x 3. (a) For what value of k is f a probability densi...

Single Variable Calculus: Early Transcendentals

Integration by Tables In Exercises 4956, use integration tables to find or evaluate the integral. 32x9x21dx,x13

Calculus of a Single Variable

For each of the following equations, solve for (a) all radian solutions and (b) t if 0t2. Give all answers as e...

Trigonometry (MindTap Course List)

True or False
Label each of the following statement as either true or false.
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Elements Of Modern Algebra

Given: m2+m3=90 BE bisects ABC CE bisects BCD Prove: ln

Elementary Geometry For College Students, 7e

Identify the type of fraction and write it in word form.
2.

Contemporary Mathematics for Business & Consumers

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Calculus: Early Transcendental Functions (MindTap Course List)

Find the area of ABC In Exercise 35, but assume that C is the reflection of B across the y-axis.

Elementary Geometry for College Students

In Exercises 21-24, find the effective rate corresponding to the given nominal rate. 5/year compounded quarterl...

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding Parametric EquationsIn Exercises 1724, find a set of parametric equations of the line with the given ch...

Multivariable Calculus

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Calculus (MindTap Course List)

The figure at the right shows one point P on a conic and the distances of P to the focus and the directrix of a...

Study Guide for Stewart's Multivariable Calculus, 8th

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

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Statistics for Business & Economics, Revised (MindTap Course List)

In addition to the key words, you should also be able to define each of the following terms: descriptive resear...

Research Methods for the Behavioral Sciences (MindTap Course List)

The accompanying time series plot of movie box office totals (in millions of dollars) over 18 weeks of summer f...

Introduction To Statistics And Data Analysis

Briefly explain why large variance within treatments is a problem in a between subjects experiment.

Research Methods for the Behavioral Sciences (MindTap Course List)

Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither. x=y23,3(y3)+x=0...

College Algebra (MindTap Course List)

Determine the value of angle A in degrees and minutes for each of the given functions. Round the answers to the...

Mathematics For Machine Technology

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STATISTICS F/BUSINESS+ECONOMICS-TEXT