CALCULUS EARLY TRANS.LLF W/WEBASSGN CODE
9th Edition
ISBN: 9780357537305
Author: Stewart
Publisher: CENGAGE L
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Textbook Question
Chapter 16.1, Problem 22E
Match the
22.
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Ministry of Higher Education &
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Babylon University
College of Engineering-
musayab
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Subject :Numerical Analyses
Stage: Third
Time: 90 min
Date: 25-4-2023
2nd month exam/2nd semester (2022-2023)
Note: Answer all questions, all questions have same degree.
Q1:Given the values
X
5
7
11
13
17
F(x)
150
392
1452
2366
5202
Evaluate f(9),using Newton's divided difference formula
Q2:A slider in a machine moves along a fixed straight rod.its distance (x cm)
along the rod is given below for various values of the time.Find the velocity
and acceleration of the slider when t=0.3 seconds.
t(seconds) 0
X (cm)
30.13
0.1
31.62
0.2 0.3 0.4 0.5 0.6
32.87 33.64 33.95 33.81 33.24
Q3:From the following table,find the area bounded by the curve and x-
axis,between the ordinates x=7.74 to x=7.52 using Simpson's 1/3 rule.
X
y=f(x)
7.47 7.48
1.93 1.95
7.49
1.98
7.50 7.51 7.52
2.01 2.03 2.06
Q4:Given
y+x
with initial condition y=1 at x=0;find (y) for x=0.1 by
Euler's method.…
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a
Which of the following is converge, and which diverge? Give reasons for your answers
with details. When your answer then determine the convergence sum if possible.
1Σn=1 (2-") n°
3" 6"
Chapter 16 Solutions
CALCULUS EARLY TRANS.LLF W/WEBASSGN CODE
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 - 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 - 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 - 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 - Sketch the vector field F by drawing a diagram...Ch. 16.1 - Match the vector fields F with the plots labeled...Ch. 16.1 - Match the vector fields F with the plots labeled...Ch. 16.1 - Match the vector fields F with the plots labeled...Ch. 16.1 - Match the vector fields F with the plots labeled...Ch. 16.1 - Match the vector fields F with the plots labeled...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 - Use graphing software to plot the vector field...Ch. 16.1 - Let F(x)=r22rx , where x=x,y and r=x . Use...Ch. 16.1 - Find the gradient vector field of f. 21. f(x, y) =...Ch. 16.1 - Find the gradient vector field of f. 22. f(s, t) =...Ch. 16.1 - Find the gradient vector field of f. 23. f(x, y,...Ch. 16.1 - Find the gradient vector field of f. 24. f(x, y,...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 - 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 - Prob. 34ECh. 16.1 - Prob. 35ECh. 16.1 - Plot the gradient vector field of f together with...Ch. 16.1 - A particle moves in a velocity field V(x, y) = x2,...Ch. 16.1 - At time t = 1, a particle is located at position...Ch. 16.1 - Prob. 39ECh. 16.1 - Prob. 40ECh. 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 - Prob. 8ECh. 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 field shown in the figure. (a)...Ch. 16.2 - The figure shows a vector field F and two curves...Ch. 16.2 - Prob. 21ECh. 16.2 - Prob. 22ECh. 16.2 - Evaluate the line integral C F dr, where C is...Ch. 16.2 - Evaluate the line integral C F dr, where C is...Ch. 16.2 - Use a calculator or computer to evaluate the line...Ch. 16.2 - Use a calculator or computer to evaluate the line...Ch. 16.2 - Prob. 34ECh. 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 - Prob. 37ECh. 16.2 - Prob. 38ECh. 16.2 - If a wire with linear density (x, y) lies along a...Ch. 16.2 - If a wire with linear density (x, y, z) lies along...Ch. 16.2 - Find the work done by the force field F(x, y) = x...Ch. 16.2 - Find the work done by the force field F(x, y) = x2...Ch. 16.2 - Find the work done by the force field F(x, y, z) =...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 - Prob. 46ECh. 16.2 - A 160-lb man carries a 25-lb can of paint up a...Ch. 16.2 - Prob. 48ECh. 16.2 - (a) Show that a constant force field does zero...Ch. 16.2 - Prob. 50ECh. 16.2 - Prob. 51ECh. 16.2 - Prob. 52ECh. 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,...Ch. 16.3 - Prob. 13ECh. 16.3 - Prob. 14ECh. 16.3 - Prob. 15ECh. 16.3 - Prob. 18ECh. 16.3 - (a) Find a function f such that F = f and (b) use...Ch. 16.3 - (a) Find a function f such that F = f and (b) use...Ch. 16.3 - Prob. 23ECh. 16.3 - (a) Find a function f such that F = f and (b) use...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 - Prob. 33ECh. 16.3 - Let F = f, where f(x, y) = sin(x 2y). Find...Ch. 16.3 - Show that if the vector field F = P i + Q j + R k...Ch. 16.3 - Prob. 36ECh. 16.3 - Determine whether or not the given set is (a)...Ch. 16.3 - Determine whether or not the given set is (a)...Ch. 16.3 - Prob. 39ECh. 16.3 - Determine whether or not the given set is (a)...Ch. 16.3 - Let F(x, y) = yi+xjx2+y2 (a) Show that P/y=Q/x....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 Green's Theorem to evaluate the line integral...Ch. 16.4 - Use Green's 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 Green's Theorem to evaluate cFdr . (Check the...Ch. 16.4 - Use Green's Theorem to evaluate cFdr . (Check the...Ch. 16.4 - Use Green's Theorem to evaluate CFdr . (Check the...Ch. 16.4 - Use Green's Theorem to evaluate CFdr . (Check the...Ch. 16.4 - Prob. 17ECh. 16.4 - Use Green's Theorem to evaluate CFdr . (Check the...Ch. 16.4 - Prob. 19ECh. 16.4 - Prob. 20ECh. 16.4 - Prob. 21ECh. 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 - Prob. 24ECh. 16.4 - (a) If C is the line segment connecting the point...Ch. 16.4 - Let D be a region bounded by a simple closed path...Ch. 16.4 - Use Exercise 26 to find the centroid of a...Ch. 16.4 - Prob. 28ECh. 16.4 - Prob. 29ECh. 16.4 - Prob. 30ECh. 16.4 - Use the method of Example 5 to calculate C F dr,...Ch. 16.4 - Calculate C F dr, where F(x, y) = x2 + y, 3x y2...Ch. 16.4 - If F is the vector field of Example 5, show that C...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...Ch. 16.5 - Find (a) the curl and (b) the divergence of the...Ch. 16.5 - Find (a) the curl and (b) the divergence of the...Ch. 16.5 - Find (a) the curl and (b) the divergence of the...Ch. 16.5 - Find (a) the curl and (b) the divergence of the...Ch. 16.5 - Prob. 6ECh. 16.5 - Find (a) the curl and (b) the divergence of the...Ch. 16.5 - Find (a) the curl and (b) the divergence of the...Ch. 16.5 - Prob. 9ECh. 16.5 - Prob. 10ECh. 16.5 - Prob. 11ECh. 16.5 - Prob. 12ECh. 16.5 - (a) Verify Formula 3 for f(x,y,z)=sinxyz . (b)...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 - Is there a vector field G on 3 such that curl G =...Ch. 16.5 - Is there a vector field G on 3 such that curl G =...Ch. 16.5 - Show that any vector field of the form F(x, y, z)...Ch. 16.5 - Show that any vector field of the form F(x, y, z)...Ch. 16.5 - Prove the identity, assuming that the appropriate...Ch. 16.5 - Prob. 26ECh. 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 = x i + y j + z k and r = |r|. 30. Verify...Ch. 16.5 - Prob. 33ECh. 16.5 - Let r = x i + y j + z k and r = |r|. 32. If F =...Ch. 16.5 - Use Greens Theorem in the form of Equation 13 to...Ch. 16.5 - Prob. 36ECh. 16.5 - Prob. 37ECh. 16.5 - Use Green's first identity to show that if f is...Ch. 16.5 - Prob. 41ECh. 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 - Prob. 4ECh. 16.6 - Prob. 5ECh. 16.6 - Prob. 6ECh. 16.6 - Prob. 7ECh. 16.6 - Prob. 9ECh. 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 - Prob. 17ECh. 16.6 - Match the equations with the graphs labeled IVI...Ch. 16.6 - Find a parametric representation for the surface....Ch. 16.6 - Prob. 20ECh. 16.6 - Find a parametric representation for the surface....Ch. 16.6 - Find a parametric representation for the surface....Ch. 16.6 - Find a parametric representation for the surface....Ch. 16.6 - Find a parametric representation for the surface....Ch. 16.6 - Find a parametric representation for the surface....Ch. 16.6 - Find a parametric representation for the surface....Ch. 16.6 - Prob. 27ECh. 16.6 - Prob. 28ECh. 16.6 - Prob. 29ECh. 16.6 - Find parametric equations for the surface obtained...Ch. 16.6 - Prob. 31ECh. 16.6 - Prob. 32ECh. 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 - Prob. 37ECh. 16.6 - Find an equation of the tangent plane to the given...Ch. 16.6 - Find the area of the surface. 39. The part of the...Ch. 16.6 - Prob. 40ECh. 16.6 - Find the area of the surface. 41. The part of the...Ch. 16.6 - Find the area of the surface. 42. The part of the...Ch. 16.6 - Find the area of the surface. 43. The surface z =...Ch. 16.6 - Find the area of the surface. 44. The part of the...Ch. 16.6 - Find the area of the surface. 45. The part of the...Ch. 16.6 - Prob. 46ECh. 16.6 - Find the area of the surface. 47. The part of the...Ch. 16.6 - Find the area of the surface. 48. The helicoid (or...Ch. 16.6 - Find the area of the surface. 49. The surface with...Ch. 16.6 - Find the area of the surface. 50. The part of the...Ch. 16.6 - Prob. 51ECh. 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 - Prob. 59ECh. 16.6 - (a) Show that the parametric equationsx = acosh u...Ch. 16.6 - Find the area of the part of the spherex2+y2+ z2=...Ch. 16.6 - The figure shows the surface created when the...Ch. 16.6 - Find the area of the part of the spherex2+y2+ z2 =...Ch. 16.7 - LetSbe the surface of the box enclosed by the...Ch. 16.7 - A surface S consists of the cylinderx2+ y2=1, 1 z...Ch. 16.7 - Prob. 3ECh. 16.7 - Suppose thatf(x, y,z)=g(), where g is a function...Ch. 16.7 - Evaluate the surface integral. 6. s xyz dS, Sis...Ch. 16.7 - Evaluate the surface integral. 7. s y dS,Sis the...Ch. 16.7 - Evaluate the surface integral. 8.s (x2+ y2)dS, Sis...Ch. 16.7 - Evaluate the surface integral. 9. s x2yz dS, Sis...Ch. 16.7 - Evaluate the surface integral. 10. s xz dS, S is...Ch. 16.7 - Evaluate the surface integral. 11. s x dS, S is...Ch. 16.7 - Evaluate the surface integral. 12. s y dS, S is...Ch. 16.7 - Evaluate the surface integral. 13. s z2dS, S is...Ch. 16.7 - Evaluate the surface integral. 14. s y2z2 dS, S is...Ch. 16.7 - Evaluate the surface integral. 16 s y2 dS, S is...Ch. 16.7 - Evaluate the surface integral. 17. s (x2z +...Ch. 16.7 - Evaluate the surface integral. 18. s (x + y + z)...Ch. 16.7 - Evaluate the surface integral. 20. s (x2 + y2 +...Ch. 16.7 - Evaluate the surface integral s F dS for the...Ch. 16.7 - Evaluate the surface integral s F dS for the...Ch. 16.7 - Evaluate the surface integral s F dS for the...Ch. 16.7 - Evaluate the surface integral s F dS for the...Ch. 16.7 - Evaluate the surface integral s F dS for the...Ch. 16.7 - F(x,y,z)=yz, S consists of the paraboloid...Ch. 16.7 - Evaluate the surface integral s F dS for the...Ch. 16.7 - Prob. 29ECh. 16.7 - Prob. 30ECh. 16.7 - Find a formula for s F dS similar to Formula 10...Ch. 16.7 - Find the center of mass of the hemisphere x2 + y2...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...Ch. 16.7 - Prob. 43ECh. 16.7 - Prob. 44ECh. 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 - Prob. 48ECh. 16.7 - Let F be an inverse square field, that is, |F(r) =...Ch. 16.8 - Use Stokes Theorem to evaluate s curl F dS. 2....Ch. 16.8 - Use Stokes Theorem to evaluate s curl F dS. 3....Ch. 16.8 - Use Stokes Theorem to evaluate s curl F dS. 4....Ch. 16.8 - F(x, y, z) = xyz i + xy j + x2yz k. S consists of...Ch. 16.8 - F(x,y,z)=exyi+exzj+x2zk S is the half of the...Ch. 16.8 - Use Stokes Theorem to evaluate c F dr. In each...Ch. 16.8 - Use Stokes Theorem to evaluate c F dr. In each...Ch. 16.8 - Use Stokes' Theorem to evaluate CFdr . In each...Ch. 16.8 - Use Stokes Theorem to evaluate c F dr. In each...Ch. 16.8 - F(x,y,z)=yx2,xy2,exy,C is the circle in the...Ch. 16.8 - F(x,y,z)=zexi+zy3j+xz3k C is the circle...Ch. 16.8 - F(x,y,z)=x2yi+x3j+eztan1zk C is the curve with...Ch. 16.8 - F(x,y,z)=x3z,xy,y+z2,C is the curve of...Ch. 16.8 - (a) Use Stokes Theorem to evaluate c F dr, where...Ch. 16.8 - (a) Use Stokes Theorem to evaluate c F dr, where...Ch. 16.8 - Verify that Stokes Theorem is true for the given...Ch. 16.8 - Verify that Stokes Theorem is true for the given...Ch. 16.8 - Verify that Stokes Theorem is true for the given...Ch. 16.8 - Prob. 20ECh. 16.8 - A particle moves along line segments from the...Ch. 16.8 - Evaluate c (y + sin x) dx + (z2 + cos y) dy + x3...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 - Prob. 13ECh. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Prob. 16ECh. 16.9 - Use the Divergence Theorem to calculate the...Ch. 16.9 - Use the Divergence Theorem to evaluate s F dS,...Ch. 16.9 - Let F(x, y, z) = z tan-1(y2) i + z3 ln(x2 + 1) j +...Ch. 16.9 - Prob. 21ECh. 16.9 - (a) Are the points P1 and P2 sources or sinks for...Ch. 16.9 - Prob. 23ECh. 16.9 - Prob. 24ECh. 16.9 - Verify that div E = 0 for the electric field...Ch. 16.9 - Prob. 26ECh. 16.9 - Prove each identity, assuming that S and E satisfy...Ch. 16.9 - Prob. 28ECh. 16.9 - Prob. 29ECh. 16.9 - Prove each identity, assuming that S and E satisfy...Ch. 16.9 - Prob. 31ECh. 16.9 - Prove each identity, assuming that S and E satisfy...Ch. 16.9 - Prob. 33ECh. 16.9 - Prob. 34ECh. 16 - What is a vector field? Give three examples that...Ch. 16 - Prob. 2CCCh. 16 - Prob. 3CCCh. 16 - (a) Define the line integral of a vector field F...Ch. 16 - Prob. 5CCCh. 16 - Prob. 6CCCh. 16 - Prob. 7CCCh. 16 - Write expressions for the area enclosed by a curve...Ch. 16 - Prob. 9CCCh. 16 - Prob. 10CCCh. 16 - Prob. 11CCCh. 16 - Prob. 12CCCh. 16 - Prob. 13CCCh. 16 - Prob. 14CCCh. 16 - Prob. 15CCCh. 16 - Prob. 16CCCh. 16 - Determine whether the statement is true or false....Ch. 16 - Prob. 2TFQCh. 16 - Prob. 3TFQCh. 16 - Prob. 4TFQCh. 16 - Prob. 5TFQCh. 16 - Prob. 6TFQCh. 16 - Determine whether the statement is true or false....Ch. 16 - Prob. 8TFQCh. 16 - Determine whether the statement is true or false....Ch. 16 - Prob. 10TFQCh. 16 - Prob. 11TFQCh. 16 - Prob. 12TFQCh. 16 - Determine whether the statement is true or false....Ch. 16 - A vector field F, a curve C, and a point P are...Ch. 16 - Evaluate the line integral. 2. C x ds, C is the...Ch. 16 - Evaluate the line integral. 3. C yz cos x ds, C: x...Ch. 16 - Evaluate the line integral. 4. C y dx + (x + y2)...Ch. 16 - Evaluate the line integral. 5. C y3 dx + x2 dy, C...Ch. 16 - Evaluate the line integral. 6. C xy dx + ey dy +...Ch. 16 - Evaluate the line integral. 7. C xy dx + y2 dy +...Ch. 16 - Evaluate the line integral. 8. C F dr, where F(x,...Ch. 16 - Evaluate the line integral. 9. C F dr, where...Ch. 16 - Find the work done by the force field F(x, y, z) =...Ch. 16 - Show that F is a conservative vector field. Then...Ch. 16 - Show that F is a conservative vector field. Then...Ch. 16 - Show that F is a conservative and use this fact to...Ch. 16 - Show that F is a conservative and use this fact to...Ch. 16 - Verify that Greens Theorem is true for the line...Ch. 16 - Use Greens Theorem to evaluate C 1+x3dx + 2xydy...Ch. 16 - Prob. 17ECh. 16 - Find curl F and div F if F(x, y, z) = e-x sin y i...Ch. 16 - Show that there is no vector field G such that...Ch. 16 - If F and G are vector fields whose component...Ch. 16 - If C is any piecewise-smooth simple closed plane...Ch. 16 - If f and g are twice differentiable functions,...Ch. 16 - If f is a harmonic function, that is, 2f = 0, show...Ch. 16 - Prob. 24ECh. 16 - Find the area of the part of the surface z = x2 +...Ch. 16 - (a) Find an equation of the tangent plane at the...Ch. 16 - Evaluate the surface integral. 27. S z dS, where S...Ch. 16 - Evaluate the surface integral. 28. s (x2z +...Ch. 16 - Evaluate the surface integral. 29. S F dS, where...Ch. 16 - Evaluate the surface integral. 30. S F dS, where...Ch. 16 - Verify that Stokes Theorem is true for the vector...Ch. 16 - Use Stokes Theorem to evaluate s curl F dS, where...Ch. 16 - Use Stokes Theorem to evaluate C F dr, where F(x,...Ch. 16 - Use the Divergence Theorem to calculate the...Ch. 16 - Verify that the Divergence Theorem is true for the...Ch. 16 - Compute the outward flux of F(x, y, z) =...Ch. 16 - Let F(x, y, z) = (3x2 yz 3y) i + (x3z 3x) j +...Ch. 16 - Prob. 38ECh. 16 - Prob. 39ECh. 16 - If the components of F have continuous second...Ch. 16 - Prob. 41ECh. 16 - 1. Let S be a smooth parametric surface and let P...Ch. 16 - Find the positively oriented simple closed curve C...Ch. 16 - Let C be a simple closed piecewise-smooth space...Ch. 16 - Prove the following identity: (F G) = (F )G + (G...Ch. 16 - Prob. 6PP
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- : +0 العنوان I need a detailed drawing with explanation しじ ined sove in peaper Anoting Q4// Draw and Evaluate √√√xy-²sin(y²)dydx PU+96er Lake Ge Q3// Find the volume of the region between the cylinder 2 = y² and the xy- plane that is bounded by the planes x = 1, x = 2, y = -2, and y = 2. T Marrow_forwardUniversity of Babylon Faculty of Engineering-AIMusyab Automobile Eng. Dep. Year: 2022-2023, 2 Course, 1 Attempt Note: Answer five questions only. Stage Third Subject: Numerical Analysis Date: 2023\\ Time: 3 Hour Q1: Solve the poisson equation [Uxx + Uyy = -81xy), [arrow_forwardMinistry of Higher Education & Scientific Research Babylon University College of Engineering- Al musayab Subject :Numerical Analysis Stage:Third Time: 2 hour Automobile Department Date:26-3-2023 nd 1st month exam/2" semester (2022-2023) Note: Answer all questions, all questions have same degree. Q1: Use Newton's method to find solutions to the system with two step Take (X,Yo)=(8,10). { x35x2 + 2xy + 13 = 0 x3 + x²-14x-y-19=0 Q2/:Solve the system by Gauss-Seidel iterative method.(Perform only three iterations). 8x-3y+2z-20 4x+11y-z-33 6x+3y+12z-35 03/:Curve fit the data using a power function X 2 4 8 5 6 0.7500 0.1875 0.1200 0.0833 0.0469arrow_forwardUniversity of Babylon Faculty of Engineering-AlMusyab Automobile Eng. Dep. Year: 2022-2023, 2nd Course, 1 Attempt Stage: Third Subject: Numerical Analysis Date: 2023\\ Time: 3 Hour dy = x + yl Q5-A: Using Euler's method, find an approximate value of (y) corresponding to (x=0.3),given that[- and [y=1 when x=0].(taking h=0.1). dx (10 M) Q5-B Find a root of an equation[f(x)=x-x-1] using Newton Raphson method to an accuracy of &=0. (10 M) Q6:Using Newton's divided differences formula, evaluate f(8) given: X 4 58 7 103 11 13 Y=f(x) 48 100 900 294 1210 2028 (20 M) Lexaminer: Examiner: Good luck W Head of Department:arrow_forwardExplain the conditions under which the Radius of Convergence of the Power Series is a "finite positive real number" r>0arrow_forwardThis means that when the Radius of Convergence of the Power Series is a "finite positive real number" r>0, then every point x of the Power Series on (-r, r) will absolutely converge (x ∈ (-r, r)). Moreover, every point x on the Power Series (-∞, -r)U(r, +∞) will diverge (|x| >r). Please explain it.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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