Q: Let G = Z31, S = {1,5, 6, 25, 26, 30}. %3D %3D Prove that Cay(G, S') is normal.
A: It is given that
Q: Let {u, v} be an orthonormal set in R" and let y = v13 u + 6v. Then, y|| is
A: Here, given that u,v are orthonormal. That is: u·u=1, v·v=1, u·v=v·u=0
Q: Evaluate | Vtan a sec" zdx. O a. 2 z tani z +tani +C 2 O b. 2 tani æ + tan +C 2 Ос. 2 O c. 2 2 t…
A: To evaluate the integral, ∫tanxsec4xdx Rewrite the term sec4x=sec2x·sec2x…
Q: az az and at the point (-1, -3, -2). Suppose ry z - 94 = 4xy – z. Compute ду dz |(-1,–3,–2) az…
A: An important result from advanced calculus, called the Implicit Function Theorem,states the…
Q: Letr(t) = (t2, 1- t,4t).Calculatethederivativeofr(t) • a(t)att = 2, assumingthata(2) = (1,3,3)…
A: Given that, rt=t2, 1-t, 4t a2=1, 3, 3a'2=-1, 4, 1 Need to evaluate derivative of rt.at
Q: 2z + 5z + 14 If U(z) = evaluate u %3D Uz and (z – 1)
A: Solution :
Q: (c(2z+y), %3D ue of c in the joi F of W.
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Q: Evaluate (2z + z – i) dz J|z-il=1
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Q: 2- find if z = x + 2メッ ze %3D U COSU = u sinv
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Q: Use the method of separation of variables to solve: (ôu ôu - = 0 in (0,1) × (0,+∞), (2) u(0,t) =…
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Q: Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0,0,0) to (4, 4, 4).
A: Given path is:
Q: { (0,3), (0,1) is linearly independent in R? ylgn O Ins
A: The given vectors are (0, 3) and (0, 1) To find whether they are linearly dependent or not
Q: U = kuzx for 0 0, u(0, t) = u(L, t) = 0, u(x, 0) = x(L – x)
A: Given that, ut=kuxx , 0<x<L, t>0u0, t=uL,t=0ux, 0=xL-x This is the heat conduction problem…
Q: Let Z, = 2 cis 30° Z2 = 3elli %3D Z = In (1 + i) If Z = Z,Z, +Z3 Find IZ.
A: First we convert all expression into a+ib form then make necessary calculation.
Q: Use chain rule to find az at (u, v) = (1, 1) if
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Q: 2) Find Ow/du and ow/ov for w=xy+ yz + xz, x=u +v, y=u-v, z = uv at the point (u, v)= (1/2,1). 3…
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Q: 2 Given t = -1 and U = -1|, for which is the set {u, T, w} {d, v, 2 linearly independent?
A: Given that, u→=1-12 and v→=2-11 We have to find the vector w→ for which the set u→, v→, w→ is…
Q: Compute x 2z ds where C is the line segment C from (0,6,–1) to (4,1,5).
A: The given line segment from to can be represented parametrically as: , , and , for Using the…
Q: Compute (S ,g) where f(t)=1– 3r² , g(1)=t-ť'onV = C[0,1]. %3D
A:
Q: 4Ux+Uy=U² , U(x,0)=1/1+x²
A: In the given partial differential equation with the given initial condition. 4ux+uy=u2u(x,0)=11+x2
Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.
A: Given,f(x,y,z)=xyz As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z
Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal
A: Given rt=<t sin t+cos t,2t2,sin t -t cos y> Then vector is given by r→t=t sin t+cos…
Q: Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0, 0,0) to (1, 4, 4).
A:
Q: Let x,(t)-v(t)+sin(r), x,-vt) then x,(t)= xN-cosit) Select ones True, False
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Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is
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Q: Use the Chain Rule to find az/əs and ôz/Ət. z = tan(u/v), u = 8s + 3t, V = 3s – 8t
A: z=tanuv, u=8s+3t, v=3s−8tFormula→∂z∂t=∂z∂u⋅∂u∂t+∂z∂v⋅∂v∂t
Q: dz - Prove that : Iz%3D2 %3D z%3D2 z+1 2in.
A:
Q: Compute ƒxz and ƒzz for ƒ(x, y, z) = xyz - x2 z + yz2.
A: Given that f(x,y,z)=xyz-x2z+yz2. We need to find : i)fxz. ii)fzz.
Q: Double integrate under z=xy, above the triangle with vertices (0,1),(0,4),(1,1).
A: We have to find the volume by double integration
Q: Find the linearization L(x,y,z) of the f(x,y,z) = 6sqrtx^3+y^3+z^3 at the point (1,2,3).
A: The linearization of a function f(x,y,z) at a point (a,b,c) is given by the expression;…
Q: 1) Find ôz|ôu and ôz/ôv for z= 4e* In(y), x=ln(ucos(v)), y=usin(v) at the point (u, v) = (2, 7 | 4).…
A: Note: According to bartlrby we have to answer only first question please upload the question…
Q: f(x, y, z) = xe z2, piecewise linear path from (0, 0, 1) to (0, 2, 0) to (1, 1, 1)
A: To Determine: calculate ∫cxez2dx Given: we have piecewise linear path from (0, 0, 1) to (0, 2, 0) to…
Q: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.
A: Given P.D.E
Q: Compute 1. % 1+ vår + g2 dr, lal 2 1+ " 2. 1+ V2r-
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Q: Find aw in terms u and v if du w= In(x2+y2 +z²), x = ue" sin u, y = ue' cos u, z = ue"; (u, v) =…
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Q: b) Verify uxy = Uyx , if u = In /x² + y² . %3D %3D
A: Consider the given function. u=lnx2+y2 To verify the equation, find the derivative first with…
Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
Q: 9. For n = 1,.., n, let X, be independent r.v.'s such that P(X,=1)= p,, P(X,=0)=1-P,- %3D Under what…
A: Definition : A sequence of random variables X1, X2 , X3 converges in probability to a random…
Q: 2) Find Ow/ôu and ôw/ôv for w= xy+ yz+ xz, x=u+v, y =u –v, z = uv at the point (u, v)= (1/2,1). 3…
A: If w=f(x,y,z) and x=g(u,v) ; y=h(u,v) and z=t(u,v) then, ∂w∂u =∂w∂x.∂x∂u+∂w∂y.∂y∂u+∂w∂z∂z∂u and…
Q: 9. For n = 1,..,n, let X, be independent r.v.'s such that %3D P(X,=1)= p,, P(X,=0)=1- p,- Under what…
A: Hello! As you have posted the different questions, we are answering the first question (9). In case…
Q: Let C: |z-i=3 and I = §. dz 2z dz. Then %3D
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Q: Eveluake F.dv wlere flaiy,z) where the segnent on Cis (-',2,0) to (3,0,1)
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Q: 3,4 show that the integsal (Xy°ty%dx + 3) Independent of the path joining the peints (1,2)and 3,4).…
A: A function F is path independent if it is conservative. And if a function F is conservative then…
Q: 4. Find the work done by the force F(r,y,2) = (x,-z,2y) in moving straight from (0,0,0) to (1.1.0),…
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Q: Consider Y; = 0 + 0,X¡ + E¿, i = 1,2,..,n, e, - N(0,0), the cov(ô,Y) = %3D
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Q: Compute I ds over the path C : F(t) = (t, 2t,ť²) from (0,0,0) to (4, 4, 4).
A: The answer is given below:
Q: Uyy=4Uxx , U(0,y)=U(5,y)=U(x,0)=0 Uy(x,0)=3sin(2pi x)x)-2sin(5pi x), y>0
A:
Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D
A: Given: f(x, y, z)=ln (x+2y+3z)
Q: a- if w = f(u, v), u = x + y, v = x-y Prove that = ( - )* aw aw %3D ду du.
A:
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