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(3) Consider the motion x = X +X,ke, and let (2) dS e te) and dX 12 (a) Find the deformed element...
(a3, y3,4z3). Let Si be the disk in the 12. Consider the vector field in space...
(a3, y3,4z3). Let Si be the disk in the 12. Consider the vector field in space given by F(x, y, z) xy-plan described by x2 + y2 < 4, z = 0; and let S2 be the upper half of the paraboloid given by z 4 y2, z 2 0. Both Si and S2 are oriented upwards. Let E be the solid region enclosed by S1 and S2 (a) Evaluate the flux integral FdS (b) Calculate div F div F...
1 (a) Consider the integral dx. e32 e-91 + e-6x +1 Make the substitution u =...
1 (a) Consider the integral dx. e32 e-91 + e-6x +1 Make the substitution u = e-34 and rewrite the integral in terms of u only. DO NOT attempt to evaluate the integral. (b) Let f(x) be a function with the properties that f(0) = 1, f(2) = 2, xf(x) dx = 4 and f(x) dx = 1. / 0 Use this information to find a se xf'(2) dr.
If Si f(x)da = 12 and so f(x) = 2.8, find si f(x)dx. Question 2 1...
If Si f(x)da = 12 and so f(x) = 2.8, find si f(x)dx. Question 2 1 pts Let f(x)dx = 6, S. 8(x)dx = -4, S g(x)da = 12, g(x)dx = 9 Use these values to evaluate the given definite integral: (+1) da
Dose 1.50) dx =7 (862) dx=15 (50) dx=9. 1'e() dv=3 14F(x)-2 g(x)) dx = is an...
Dose 1.50) dx =7 (862) dx=15 (50) dx=9. 1'e() dv=3 14F(x)-2 g(x)) dx = is an odd function and is an even function Evaluate to (103dx = $(x) dx = 59(2) de T I Arial 3 (12pt] · TE E 5.00 1. P Question Completion Status: > A Moving to another question will save this response. Question 9 a , it Use Second Fundamental Theorem to find a Jo 0 ਨੰ: it = ਦੈਤ 0 , it = ਰੈੱਡ ©...
(f) If a and b are unit vectors and θ is the angle between them. prove that sin -b Prove that v2·“2 + 2,6 , where the symbol's h) have their usual meanings 12. Find the following dx dx tan'xd...
(f) If a and b are unit vectors and θ is the angle between them. prove that sin -b Prove that v2·“2 + 2,6 , where the symbol's h) have their usual meanings 12. Find the following dx dx tan'xdx (i) 1+cos x 13 Find the area enclosed between the circle 2y25 and the straight line x +y- s 14. Solve the following equations dy dy dy dx
(f) If a and b are unit vectors and θ is the...
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx...
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
5) In Goy), with inner product < 1.8>]s«g(x)dx, let S(x)=x"$(x)=x', a) Computer />; b) Find the...
5) In Goy), with inner product < 1.8>]s«g(x)dx, let S(x)=x"$(x)=x', a) Computer />; b) Find the "angle" between the two functions.
8 6. Consider two functions fand gon (2.8] such that Sf(x)dx = 12. Jo(x)dx=5. vex)dx=7, and...
8 6. Consider two functions fand gon (2.8] such that Sf(x)dx = 12. Jo(x)dx=5. vex)dx=7, and 59(x)dx = 3. Evaluate the following integrals 2 2 6 a. (58(x)dx=(Simplify your answer.)
(2) Let F-1 + rj + yk and consider the integral- , ▽ × F. т. dS where s is the surface of the paraboloid z = 1-12-y2 co...
(2) Let F-1 + rj + yk and consider the integral- , ▽ × F. т. dS where s is the surface of the paraboloid z = 1-12-y2 corresponding to z 0, and n is a unit normal vector to S in the positive z-direction (a) Apply Stokes' theorem to evaluate the integral. (b) Evaluate the integral directly over the surface S rectlv over the new surface
(2) Let F-1 + rj + yk and consider the integral- , ▽...
x = -6 28. Suppose that {$(x)dx=-6. Se (x)dx = 8 and !!) . Find ļ[3/(x)+8(*)]dx...
x = -6 28. Suppose that {$(x)dx=-6. Se (x)dx = 8 and !!) . Find ļ[3/(x)+8(*)]dx (x) dx = 8 . Finds d. 6 e. None of these a. -10 b. 11 c. 18 29. If 0-1 - 51+4 represents the rectilinear motion of a particle, the particle changes direction at what time? Assume is in seconds. a. 4.5 sec b. 2 sec C. 1.5 sec d. 2.5 sec e. None of these
(a3, y3,4z3). Let Si be the disk in the 12. Consider the vector field in space given by F(x, y, z) xy-plan described by x2 + y2 < 4, z = 0; and let S2 be the upper half of the paraboloid given by z 4 y2, z 2 0. Both Si and S2 are oriented upwards. Let E be the solid region enclosed by S1 and S2 (a) Evaluate the flux integral FdS (b) Calculate div F div F...
1 (a) Consider the integral dx. e32 e-91 + e-6x +1 Make the substitution u = e-34 and rewrite the integral in terms of u only. DO NOT attempt to evaluate the integral. (b) Let f(x) be a function with the properties that f(0) = 1, f(2) = 2, xf(x) dx = 4 and f(x) dx = 1. / 0 Use this information to find a se xf'(2) dr.
If Si f(x)da = 12 and so f(x) = 2.8, find si f(x)dx. Question 2 1 pts Let f(x)dx = 6, S. 8(x)dx = -4, S g(x)da = 12, g(x)dx = 9 Use these values to evaluate the given definite integral: (+1) da
Dose 1.50) dx =7 (862) dx=15 (50) dx=9. 1'e() dv=3 14F(x)-2 g(x)) dx = is an odd function and is an even function Evaluate to (103dx = $(x) dx = 59(2) de T I Arial 3 (12pt] · TE E 5.00 1. P Question Completion Status: > A Moving to another question will save this response. Question 9 a , it Use Second Fundamental Theorem to find a Jo 0 ਨੰ: it = ਦੈਤ 0 , it = ਰੈੱਡ ©...
(f) If a and b are unit vectors and θ is the angle between them. prove that sin -b Prove that v2·“2 + 2,6 , where the symbol's h) have their usual meanings 12. Find the following dx dx tan'xdx (i) 1+cos x 13 Find the area enclosed between the circle 2y25 and the straight line x +y- s 14. Solve the following equations dy dy dy dx
(f) If a and b are unit vectors and θ is the...
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
5) In Goy), with inner product < 1.8>]s«g(x)dx, let S(x)=x"$(x)=x', a) Computer />; b) Find the "angle" between the two functions.
8 6. Consider two functions fand gon (2.8] such that Sf(x)dx = 12. Jo(x)dx=5. vex)dx=7, and 59(x)dx = 3. Evaluate the following integrals 2 2 6 a. (58(x)dx=(Simplify your answer.)
(2) Let F-1 + rj + yk and consider the integral- , ▽ × F. т. dS where s is the surface of the paraboloid z = 1-12-y2 corresponding to z 0, and n is a unit normal vector to S in the positive z-direction (a) Apply Stokes' theorem to evaluate the integral. (b) Evaluate the integral directly over the surface S rectlv over the new surface
(2) Let F-1 + rj + yk and consider the integral- , ▽...
x = -6 28. Suppose that {$(x)dx=-6. Se (x)dx = 8 and !!) . Find ļ[3/(x)+8(*)]dx (x) dx = 8 . Finds d. 6 e. None of these a. -10 b. 11 c. 18 29. If 0-1 - 51+4 represents the rectilinear motion of a particle, the particle changes direction at what time? Assume is in seconds. a. 4.5 sec b. 2 sec C. 1.5 sec d. 2.5 sec e. None of these
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