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(1 point) Curves Cị and C2 are parametrized as follows: Ci is (z(t), y(t)) = (t,0)...
Suppose C is a curve parametrized by r(t)=<cost,sint,1> and S is the portion of z=x^2+y^2 enclosed...
Suppose C is a curve parametrized by r(t)=<cost,sint,1>
and S is the portion of z=x^2+y^2 enclosed by C, located in the
vector field F=<z,-x,y>.
25. Suppose C is the curve parametrized by F(t) = (cost, sint, 1) and S is the portion of z = x2 + y2 enclosed by C, located in the vector field F = (2, -,y). Verify Stokes' theorem. That is, find show they are, in fact, the same. fe dr and SIC (curl ) ñds...
3. Suppose x,y,z satisfy the competing species equations <(6 - 2x – 3y - 2) y(7...
3. Suppose x,y,z satisfy the competing species equations <(6 - 2x – 3y - 2) y(7 - 2x - 3y - 22) z(5 - 2x - y -22) (a) (6 points) Find the critical point (0,Ye, ze) where ye, we >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (2,0,0) is stable, where I > 0.
Let C1 be the semicircle given by z = 0,y ≥ 0,x2 + y2 = 1...
Let C1 be the semicircle given
by z = 0,y ≥ 0,x2 + y2 = 1 and C2 the semicircle given by y = 0,z ≥
0,x2 +z2 = 1. Let C be the closed curve formed by C1 and C2. Let F
= hy + 2y2,2x + 4xy + 6z2,3x + eyi. a) Draw the curve C. Choose an
orientation of C and mark it clearly on the picture. b) Use
Stokes’s theorem to compute the line integral ZC...
and C2 in the xy-planedefined by the parametric equations Consider trajectories on two curves C1:x=t?, y=t?...
and C2 in the xy-planedefined by the parametric equations Consider trajectories on two curves C1:x=t?, y=t? - <t<«. C2: x = 3t, y=t?, - <t<mo. These two trajectories are known to *intersect* at exactly two points. The origin (0,0) is one of them. And there is another one, which we'll call P. Find Pand select the choice below which gives the slope of the tangent line to the first curve at the point P. Note that only ONE of the...
(1 point) Solve the nonhomogeneous heat problem 24 = 1,+ sin(2.0), 0<I<T, u(0,t) = 0, u1,t)...
(1 point) Solve the nonhomogeneous heat problem 24 = 1,+ sin(2.0), 0<I<T, u(0,t) = 0, u1,t) = 0 u(3,0) = 3 sin(4x) uz,t) = sinx, sint Steady State Solution limuz,t) =
5. (1 point) Find constants ci, c2, and c3, such that the function y ci +...
5. (1 point) Find constants ci, c2, and c3, such that the function y ci + c2 cos(5x) + c3 sin (5x) is the solution of the initial value problem 18 y"+25yo y(0)=-5 У"(0)--20 y"(0) 50 Answert s) submitted (incorrect) 6. (1 point) Calculate the Wronskian for the following set of functions:
(1 point) Calculate the integral of f(x, y, z)-3x2 + 3уг + z6 over the curve c(t) (cost, sint, t)...
(1 point) Calculate the integral of f(x, y, z)-3x2 + 3уг + z6 over the curve c(t) (cost, sint, t) for 0 < t < π
(1 point) Calculate the integral of f(x, y, z)-3x2 + 3уг + z6 over the curve c(t) (cost, sint, t) for 0
Problem 1. Assume that F-(Fi, F2):S-R2 is a function of class C2. Show that if S is parametrized ...
Problem 1. Assume that F-(Fi, F2):S-R2 is a function of class C2. Show that if S is parametrized by x-g(t)-(cost, sint) for OSts 2m, then F2 og) (t) dt. Remark: Problem l shows that the integral las F, dz+ 쓺dy) depends only on the values of F on S. This is because we only need to know the values of Fi and F2 on aS to compute This is not obvious, because if we know the values of F2 only...
MATLAB ONLY MATLAB ONLY MATLAB ONLY MATLAB ONLY (x(t), y(t)) (t - sint, 1- cost 1....
MATLAB ONLY MATLAB ONLY
MATLAB ONLY MATLAB ONLY
(x(t), y(t)) (t - sint, 1- cost 1. (15 pts) Consider the parametrized curve 0,7] 2) (10pts) Calculate the length of (x(t), y(t)) from 0 to 7 1) (5pts) Plot the graph of parametrized curve on
(x(t), y(t)) (t - sint, 1- cost 1. (15 pts) Consider the parametrized curve 0,7] 2) (10pts) Calculate the length of (x(t), y(t)) from 0 to 7 1) (5pts) Plot the graph of parametrized curve on
Given the path C: x(t) = (cost, sint, t), 0<t<2n. Let f(t, y, z) = x2...
Given the path C: x(t) = (cost, sint, t), 0<t<2n. Let f(t, y, z) = x2 + y2 + 22. Evaluate (12 pts) f(,y,z)ds.
Suppose C is a curve parametrized by r(t)=<cost,sint,1>
and S is the portion of z=x^2+y^2 enclosed by C, located in the
vector field F=<z,-x,y>.
25. Suppose C is the curve parametrized by F(t) = (cost, sint, 1) and S is the portion of z = x2 + y2 enclosed by C, located in the vector field F = (2, -,y). Verify Stokes' theorem. That is, find show they are, in fact, the same. fe dr and SIC (curl ) ñds...
3. Suppose x,y,z satisfy the competing species equations <(6 - 2x – 3y - 2) y(7 - 2x - 3y - 22) z(5 - 2x - y -22) (a) (6 points) Find the critical point (0,Ye, ze) where ye, we >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (2,0,0) is stable, where I > 0.
Let C1 be the semicircle given
by z = 0,y ≥ 0,x2 + y2 = 1 and C2 the semicircle given by y = 0,z ≥
0,x2 +z2 = 1. Let C be the closed curve formed by C1 and C2. Let F
= hy + 2y2,2x + 4xy + 6z2,3x + eyi. a) Draw the curve C. Choose an
orientation of C and mark it clearly on the picture. b) Use
Stokes’s theorem to compute the line integral ZC...
and C2 in the xy-planedefined by the parametric equations Consider trajectories on two curves C1:x=t?, y=t? - <t<«. C2: x = 3t, y=t?, - <t<mo. These two trajectories are known to *intersect* at exactly two points. The origin (0,0) is one of them. And there is another one, which we'll call P. Find Pand select the choice below which gives the slope of the tangent line to the first curve at the point P. Note that only ONE of the...
(1 point) Solve the nonhomogeneous heat problem 24 = 1,+ sin(2.0), 0<I<T, u(0,t) = 0, u1,t) = 0 u(3,0) = 3 sin(4x) uz,t) = sinx, sint Steady State Solution limuz,t) =
5. (1 point) Find constants ci, c2, and c3, such that the function y ci + c2 cos(5x) + c3 sin (5x) is the solution of the initial value problem 18 y"+25yo y(0)=-5 У"(0)--20 y"(0) 50 Answert s) submitted (incorrect) 6. (1 point) Calculate the Wronskian for the following set of functions:
(1 point) Calculate the integral of f(x, y, z)-3x2 + 3уг + z6 over the curve c(t) (cost, sint, t) for 0 < t < π
(1 point) Calculate the integral of f(x, y, z)-3x2 + 3уг + z6 over the curve c(t) (cost, sint, t) for 0
Problem 1. Assume that F-(Fi, F2):S-R2 is a function of class C2. Show that if S is parametrized by x-g(t)-(cost, sint) for OSts 2m, then F2 og) (t) dt. Remark: Problem l shows that the integral las F, dz+ 쓺dy) depends only on the values of F on S. This is because we only need to know the values of Fi and F2 on aS to compute This is not obvious, because if we know the values of F2 only...
MATLAB ONLY MATLAB ONLY
MATLAB ONLY MATLAB ONLY
(x(t), y(t)) (t - sint, 1- cost 1. (15 pts) Consider the parametrized curve 0,7] 2) (10pts) Calculate the length of (x(t), y(t)) from 0 to 7 1) (5pts) Plot the graph of parametrized curve on
(x(t), y(t)) (t - sint, 1- cost 1. (15 pts) Consider the parametrized curve 0,7] 2) (10pts) Calculate the length of (x(t), y(t)) from 0 to 7 1) (5pts) Plot the graph of parametrized curve on
Given the path C: x(t) = (cost, sint, t), 0<t<2n. Let f(t, y, z) = x2 + y2 + 22. Evaluate (12 pts) f(,y,z)ds.
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