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a) Find the length of the curve traced by the given vector function on the indicated...
2. Find the length of the curve traced by the fiunction vector r+ej +sin +5) k...
2. Find the length of the curve traced by the fiunction vector r+ej +sin +5) k on the interval 0sts.
For each of the following vector fields, find its curl and determine if it is a...
For each of the following vector fields, find its curl and
determine if it is a gradient field.
(1 point) For each of the following vector fields, find its curl and determine if it is a gradient field. (a) F = 5(xy + 22) + 10(x2 + y2) 7+ 10(x2 + y2) k. curl F = F ? (b) Ğ = 5yzi + (52z+z2) 7+ (5xy + 2yz) k: curl Ĝ = Ğ ? (c) H = (5xy + yz)...
Finding the curvature of a vector function My Solutions > Find the curvature of the curve traced ...
use matlab
Finding the curvature of a vector function My Solutions > Find the curvature of the curve traced out by the function r(t)- tA2, 5t-1, 2tA3-t> att-1. Your Script B Save C Reset MATLAB Documentation 1 syms t 2 f- 9 10 k- Run Script
Finding the curvature of a vector function My Solutions > Find the curvature of the curve traced out by the function r(t)- tA2, 5t-1, 2tA3-t> att-1. Your Script B Save C Reset MATLAB Documentation...
Sketching a Curve In Exercises 9-12, sketch the curve represented by the vector-valued function and give...
Sketching a Curve In Exercises 9-12, sketch the curve represented by the vector-valued function and give the orientation of the curve. 2 9. r(t) = (n cost, i sin ) 10. r(t) = (1 + 2.12 - 1) 11. r(t) = (1 + 1)i + (31 - 1)j + 2tk 12. r(t) = 2 cos ti + tj + 2 sin tk 29 12. r(t) = 2 cos ti + tj + 2 sin tk
(7.5 points) Let C be the oriented closed space curve traced out by the parametrization r(t)...
(7.5 points) Let C be the oriented closed space curve traced out by the parametrization r(t) = (cost, sint, sin 2t), 0<t<27 and let v be the vector field in space defined by v(x, y, z) = (et - yº, ey + r), e) (a) Show that C lies on the cylinder x2 + y2 = 1 and the surface z = 2cy. (b) This implies that C can be seen as the boundary of the surface S which is...
1.) (8 pts.) Consider the vector field F(t, y, z) = (3cʻz + 3 + yzbi...
1.) (8 pts.) Consider the vector field F(t, y, z) = (3cʻz + 3 + yzbi – (22 - 12)ī + (23 – 2yz +2 + xy)k Find a scalar function f, which has a gradient vector equal to F, or determine that this is impossible.
Sketch the space curve. Interval Vector-Valued Function r(t) = -ti + 5tj + 2tk [0, 1]...
Sketch the space curve. Interval Vector-Valued Function r(t) = -ti + 5tj + 2tk [0, 1] 6 2 2 6 6 22 7. 4 2 Find its length over the given interval. Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize f(x, y) = 2x + 2xy + y Constraint: 2x + y = 200 file 40.80
Show all work and use correct notation for full credit. Stokes' Theorem: Let S be an...
Show all work and use correct notation for full credit. Stokes' Theorem: Let S be an orientable, piecewise smooth surface, bounded by a simple closed piecewise smooth curve C with positive orientation. Let F be a vector field with component functions that have continuous partial derivatives on an open region in R3 that contains S. Then | | curl(F) . ds F-dr = where curl(F) = ▽ × F. (2 Credits) Let S be the cone given by {(z, y,...
Find the absolute extrema of the given function on the indicated closed and bounded set R....
Find the absolute extrema of the given function on the indicated closed and bounded set R. f (x,y) = 2x2 + 3y2 – 3x; R is the disk x² + y2 s 16. Enter the exact answers in the form of improper fractions, if necessary, Absolute maximum Edit Absolute minimum: Edit
Evaluate the line integral ∫ F *dr where C is given by the vector function r(t)....
Evaluate the line integral ∫ F *dr
where C is given by the vector function
r(t).
F(x, y, z) =
(x + y2) i +
xz j + (y + z)
k,
r(t) =
t2i +
t3j − 2t
k, 0 ≤ t ≤ 2
2. Find the length of the curve traced by the fiunction vector r+ej +sin +5) k on the interval 0sts.
For each of the following vector fields, find its curl and
determine if it is a gradient field.
(1 point) For each of the following vector fields, find its curl and determine if it is a gradient field. (a) F = 5(xy + 22) + 10(x2 + y2) 7+ 10(x2 + y2) k. curl F = F ? (b) Ğ = 5yzi + (52z+z2) 7+ (5xy + 2yz) k: curl Ĝ = Ğ ? (c) H = (5xy + yz)...
use matlab
Finding the curvature of a vector function My Solutions > Find the curvature of the curve traced out by the function r(t)- tA2, 5t-1, 2tA3-t> att-1. Your Script B Save C Reset MATLAB Documentation 1 syms t 2 f- 9 10 k- Run Script
Finding the curvature of a vector function My Solutions > Find the curvature of the curve traced out by the function r(t)- tA2, 5t-1, 2tA3-t> att-1. Your Script B Save C Reset MATLAB Documentation...
Sketching a Curve In Exercises 9-12, sketch the curve represented by the vector-valued function and give the orientation of the curve. 2 9. r(t) = (n cost, i sin ) 10. r(t) = (1 + 2.12 - 1) 11. r(t) = (1 + 1)i + (31 - 1)j + 2tk 12. r(t) = 2 cos ti + tj + 2 sin tk 29 12. r(t) = 2 cos ti + tj + 2 sin tk
(7.5 points) Let C be the oriented closed space curve traced out by the parametrization r(t) = (cost, sint, sin 2t), 0<t<27 and let v be the vector field in space defined by v(x, y, z) = (et - yº, ey + r), e) (a) Show that C lies on the cylinder x2 + y2 = 1 and the surface z = 2cy. (b) This implies that C can be seen as the boundary of the surface S which is...
1.) (8 pts.) Consider the vector field F(t, y, z) = (3cʻz + 3 + yzbi – (22 - 12)ī + (23 – 2yz +2 + xy)k Find a scalar function f, which has a gradient vector equal to F, or determine that this is impossible.
Sketch the space curve. Interval Vector-Valued Function r(t) = -ti + 5tj + 2tk [0, 1] 6 2 2 6 6 22 7. 4 2 Find its length over the given interval. Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize f(x, y) = 2x + 2xy + y Constraint: 2x + y = 200 file 40.80
Show all work and use correct notation for full credit. Stokes' Theorem: Let S be an orientable, piecewise smooth surface, bounded by a simple closed piecewise smooth curve C with positive orientation. Let F be a vector field with component functions that have continuous partial derivatives on an open region in R3 that contains S. Then | | curl(F) . ds F-dr = where curl(F) = ▽ × F. (2 Credits) Let S be the cone given by {(z, y,...
Find the absolute extrema of the given function on the indicated closed and bounded set R. f (x,y) = 2x2 + 3y2 – 3x; R is the disk x² + y2 s 16. Enter the exact answers in the form of improper fractions, if necessary, Absolute maximum Edit Absolute minimum: Edit
Evaluate the line integral ∫ F *dr
where C is given by the vector function
r(t).
F(x, y, z) =
(x + y2) i +
xz j + (y + z)
k,
r(t) =
t2i +
t3j − 2t
k, 0 ≤ t ≤ 2
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