Let U = {a, b, c, d, e, f,g, h}, A = {a, c, f, g}, B = {a,e}, C = {b,h}, calculate: a. ΑΘΒ b. В@А

Q: If f = xi + yj + zk, l7I = r,and i=, then show that grad () =

A: 1. Gradf=(dfdxi^ + dfdyj^ + dfdzk^ )      2.  dxndx = n xn-1 3. r = x2+ y2 +z2

Q: Given that w= f (x,u,v),u= g(x, v, y) and v=h(x, y). = f„8, + f,h, + f„g,h, ôy Show that

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Q: Given: z = x² + xy³, x = uv² +w³, y=u+vew əz Find when u = 1, v = -1, w=0 Əv

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Q: Group C QI: For Ā = x āx + y ãy + z āz and B = 3x āx + 4y ãy + 2z āz Find the following a) Č = ĀxB…

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Q: Given: z = a' + æy", r = uv² + w®, y = u + ve" az Find when u = 2, v = – 3, w = 0 dv

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Q: Given u=excos(y) and v=exsin(y) calculate: ∂x , ∂y…

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Q: S CO a) A, BE {points} = AB E Q. b) A, BE {points} AB E R. ) A, BE {points} ^ |{A, B}| =1= AB = 0.…

A: Note: According to Bartleby guidelines; for more than three questions asked only the first three are…

Q: calculate r(t) and T(t), and evaluate T(1).  r(t) = (et, t2)

A: rt=et, t2 Differentiating with respect to t, we get r't=detdt,  dt2dt=et,  2t Now,…

Q: If X and Y are independent RVs, then E(YIX) - F(Y) nd F(Y10

A: X and Y are independent then joint distribution of X and Y is  f(x,y)=f(x)f(y)

Q: If f(x, y) = xsiny + e" , then V f(x, y) = (0, e'). Select one: True OFalse

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Given f(r, y) = yln(5z+ y), find .(e, v) - 1,(2, u) = %3D

A: We have to find derivative

Q: "en J(2, 9) 5y), find =(z, y) = (z, y) = -(z, y) = %3D

A: We wil find the second order partial derivative.

Q: for for w= rs ,Y=uV S=uーv, find and Jw

A: Given w=rsr2+s2, r=uv, s=u-2v To find  ∂w∂u and ∂w∂v By chain rule,…

Q: Acellus When DE || AB and DE 1 EB AB [?] EB A C neither, they are skew lines Copyright 2003 - 2021…

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Q: Evaluate O xy dx + x°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

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Q: Let z = ety, where x = Vuv and y . Find dz in terms of u and v.

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Q: Given u(x, t) = t°e¯ï, compute:

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Q: Let W = {a + bX + cX² + dX³; a – b = 0, c = 4b,}. Then the dimension of W is %3D

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Q: ו הי ןווה (t) = (2cos t)i + (2sin t)j + (5 t)k, Ostsa

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Q: Evaluate S, y dv with E = {(x, y,z): 0 <x< 3, 0< y < x, (x – y) < z < (x + y)} %3D

A: Use triple integration

Q: A = (C = { z = x+yi : x, y E R, i² = -1},+), (a+bi)+(c+di) = (a+c)+(b+d)i • B = iR = { iy : y E R }

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Q: , find the Jacobian ?(x, y)?(u, v) for the indicated change of variables x = uv − 2u, y = uv

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Q: Let D, E ⊂ C be starshaped w.r.t the same z∗ ∈ D ∩ E. Show that D ∪ E, D ∩ E are starshaped

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (c) z = x2 + 2y2 ; x = es - et, y = es + et

A: Formula to find the partial derivatives helps to find the partial derivatives of the function with…

Q: Evaluate O xy°dx + x²dy, where C is the rectangle with vertices (0,0), (6,0), (6,4), and (0,4)

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Q: Find f, and f, and evaluate each at the given point. f(x, y) = arctan () (6, -6) %3D y,x, y) – fx(6,…

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Q: Given w = f(x, Y, z) =

A: Given,                                   w=f(x, y, z)=4x2+y2+4z2and…

Q: W Find aunit vetor orthegonal to A in The plane of Band c if ArZi-j+K B-i+j+K +j-2k

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Q: If z = u sin(u?) and u = Vt, find ) If z = x² + y², x = u+ v² and y = u² – v, find and

A: Given: (a) z = u sin ( u2 )  (b) z = x2 + y2  , x and y values given

Q: If & = {(z, y, z) | 1< * < 2, z < y < 2a, 0 < z < z +2y} then: SI. 3zz dV ニ

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Q: Find a and b such that v au + bw, where where u (1, 2) and w - v- (0, 6)

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Q: Given: z = = x* + zy°, * = ww* + w, y = u +ve" a z Find when u = - 3, v = 2, w =

A: Given: z=x4+xy3x=uv4+w4y=u+vew The objective is to find ∂z∂u, when u=-3, v=2, w=0

Q: Evaluate O xy dx + x°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3).

A: The solution is given by using greens theorem as follows

Q: d) If U = X + Y and V = Y – X, find i) The Jacobian value of U and V J(U,V)

A: Solution

Q: Given u = i- j, and v = j+ k, determine the magnidue of u +v and - 2v.

A: By sum of two vectors we have  u+v=(i-j)+(j+k) u+v=i+k -2v=-2(j+k)=-2j-2k

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. v), y = (u + v) X = -

A: The formula for the Jacobian is: ∂(x,y)∂(u,v)=∂x∂u∂x∂v∂y∂u∂y∂v

Q: Show that if X and Y are independent rv's, then E(XY) = E(X) · E(Y)

A: we have given that, x and y are independent random variables, then, we will prove, E(XY)= E(X).E(Y),

Q: EXERCISE 3. Calculate a x b when la = between 1, b| = 3 and the angle a and b is 0 = 30° %3D

A: Given that |a|=1 and |b|=3 The angle between a and b is 30°

Q: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

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Q: Exercise.8 Find: P,(x), Pg(x), L, Pa(x) Pg(x) dx , LIP,(x)l² dx

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Q: y =c,J,(x) +c_Y, (x) .A y=c,J,(x) +c,Y, (y) .B y=c,,(x)+c_y,(x) .C y=c,J,(y) +c_Yn(x)

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Suppose z is in the first quadrant and w= i. Discuss the quadrant in which wz could be located.

A: Given z is in the first quadrant , hence the real part and imaginary part of zis positive Let z =…

Q: If points D, E, and F are collinear, then DE + EF = DF.

A: DE+EF=DF [Segment Addition Postulate ] False- it could happen just not in all cases. Maybe they…

Q: 1. If AM = 10, then TC =? %3D A. 5 В. 10 C. 15 D. 20 W/ 2. JH || TC and mJH = 40°, mJT = H A. 40° B.…

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Q: a) What does ds(u, v) measure? (b) What does dm(u, v) measure?

A: To find: a) measure of ds(u, v) . (b) measure of dm(u, v).

Q: Given z = arctan (), Find az/ay

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Q: Let F = (x + y) exp(x), x = ln(u), and y = v. Find Your answer should be in terms of , y, U, and v.…

A: We have to find partial derivative

Q: f(z, y) – zsiny +e, then Vf(r, y) (0, e").

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Q: For what values of aare u and v orthogonal?

A: Consider the given vectors  u=11-2  and  v=a-12 Write the vectors in row form u=1,1,-2  and…