Let UsX +Sinx Deter of X 0n [0,)where ļ Find . derivalire fa 2x+1 x²+7 te tn 6x+

Q: a2 If a;j = aji (ajX;X;) əxyəx; are constant, calculate %3D

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Q: For F(x, y, z) = x²z² i+ sinx z²j+zx²y*k, find div F and curl F.

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Q: 2- find if z = x + 2メッ ze %3D U COSU = u sinv

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Q: Prove that: cscz- cot z = 1 2. 2. %3D

A: We need to prove the identity  csc2z-cot2z=1

Q: Use the chain rule to evaluate fu and f, at (u,v)=(2,-2) where f(x,y,z)=y³+xz² and x=x(u,v)=u+v²,…

A: Concept: The chain rule for the function f (x,y,z) is  dfdu=∂f∂x∂x∂u+∂f∂y∂y∂u+∂f∂z∂z∂u…

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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Q: Utt = 8uxx for 0 < x < ™ u(x, 0) = x² u(x, 0) = 1/2cos(8x) Uz(0, t) = u„(T, t) = 0 %3D II

A: The given P.D.E is                            utt=8uxx for…

Q: Find the work done by the force F = x²yi– xy²j along the paths shown from (1, 1) to (4, 2). (4, 2) a…

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Q: Find div F and curl F if F(x, y, z) = 13y'z4i – 16x4z10j – 3xy'k. - - div F= curl F=

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Q: Let u = cos(r + y), x = 2st +t and y = t – 2s. Use the chain rule theorem to compute du for du and…

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Q: Let X ={li2,3,4,53 Determime the tnith valve Of each of the pioparitons. %3D a) (bx EX)x + x? <3Q t.

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Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=&lt;t sin t+cos t,2t2,sin t -t cos y&gt; Then vector is given by r→t=t sin t+cos…

Q: Let z(a, y) = 7x – 6y where x = - 7s – 4t & y = – 2s + 8t. %3D %3D az Calculate as az by first…

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Q: Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).

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Q: dz - Prove that : Iz%3D2 %3D z%3D2 z+1 2in.

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Q: Suppose F (x, y) = (2xe-", 2y – a²e="} (a) Find a scalar function f (x, y) such that F = Vf (b) Use…

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Q: 3. Find the circulation of F 2xi + 2zj +2yk around closed contour %3D

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Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

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Q: u,v) = ve*tv, and z(u,v) = (u+v)cos v?. OG nd and by using multivariable Chain Rule method. du u=1

A: Given: Gx, y, z=e2x+y+3zxu, v=u lnu+vyu, v=veu+vzu, v=u+v cos v2  To Find: To find  ∂G∂uu=1v=0  and…

Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: Let xbe inner Product and ||x1|=|ly|| = 1 x+y Lix.y ? why?

A: Given that X is an real inner product space. x ,y be two unit vector from X then need to show that…

Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y + z+ w= 6 3x…

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Q: Find div F and curl F if F(x, y, z) = 4y³z'i – 11a"z°j – 4xy°k. - -

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Q: Find the Second appoximation for the System. X Sin y at (xo,,)= (1, 1). y=Cosx

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Q: let f (x, y) = x² + xy + y². Using the chain rule, calculate %3D af -(u(x, y), v(x, y)) being u = v…

A: Given that                                   f(x, y)=x2+xy+y2 And also we have…

Q: Use Cramer's rule to solve for y without solving for x, z, and w. 5 x + y + z + W = -7 5x + 3y - z +…

A: Here we have to use cramer rule for solving the system of linear equations

Q: Show that the line integral 22 +2ry) dx + x? dy + 2xz dz, is independent of path in R, where C runs…

A: We will find out the required values.

Q: Suppose that u € C² (R²) and u(x, y) = 0 everywhere on the boundary of the square ((x,y): 0≤x≤ R,0 ≤…

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Q: that ulx,y) = 42 Cos 3y is the particulas -3X prove Solution of Uxx+Uyy =0 u cx, 플) =0 where…

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Q: Find the bounded อน əx solution of อน 2 + U if U(x, 0) = 6e-3x. at

A: We have ∂u∂x=2∂u∂t+u  The initial condition is ux,0=6e-3x Now, ∂u∂x=2∂u∂t+u can be written as…

Q: | Let u = x*y + y°23 where x = rse', y = rs²e=t, = 2, 8 = 1 and t = 0, by using Chain Rule. p2 Sint.…

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Q: Find up +Uy given that u (x,Y)s. (x,x)s

A: Given that ux, y=tanx3+mx2y2+my4m-x2-y2 To find ux+uy we follow the following steps calculate…

Q: bot A de groutne conitant. est Cheafuntis uh that f cark3 and f'4)=-s. g(xl=In (f(x)) + A conx)

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Q: . Show that the function u = p(ry) + Vry v(y/x) provides the quation = 0. ду? %3D dx²

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Q: Let F(x, y, z) = (8x7 In(7y² + 4) + 6z') i + ( +4 14yx + 4z)j + (42xz°+ 4y – 27 sin 7z) k and let…

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Q: find div and curl F F(x,y,z)= 7y3z2i- 8x2z5j-3xy4k F(x,y,z) = exyi-cosy j +sin2 z k

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Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Dx(f)=8x+5 Apply integration both side  ∫Dx(f)dX=∫(8x+5)dx   f(x)=(8x2)/2 + 5x +c (here c is the…

Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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Q: Use the Chain Rule to find zz and zy given sin(u) tan(v), u = 3x + y, and v = x – y. %3D

A: Given z = sin(u) tan(v)where u = 3x + yv = x - y

Q: Find div F and curl F if F(x, y, z) = 9y%z®i – 4x°z1°j – 5xy°k. - -

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Q: Let f(z) = sin(z'). %3D s'(z) = 3 coslx 3)) 2. 3x cos(X %3D S'(4) = 0

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Q: Express dw/dr and dw/as as functions of r and s using chain rule w = In(x + y + z*), x = re sin r, y…

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Q: Solve for z using cramer's rule.  2x-y-z=4 4x+y+z=2 3y+z=2

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Q: Find div F and curl F if F(x, y, z) = 16y°z³i – 9x°z°j – 7xy'k. - - div F= curl F=

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Q: Prove that the integral: √ [2xyz² dx + (x²z² + z cos yz)dy + (2x²yz + y cos yz)dz ] Is independent…

A: The given integral is ∫C2xyz2dx+x2z2+zcos yzdy+2x2yz+y cos yzdz. The objective is to prove that the…

Q: If Ø : R3 → R3 be defined as Ø (x,y,z) = (2x, 4x –y,2x+ 3yz) then show that Ø is invertible. %3D

A: Given that ϕ:R3→R3 is defined as ϕx,y,z=2x,4x-y,2x+3yz. Now, ϕ is invertible if ϕ is one-one and…

Q: 6. Let f(u, v) = u sin(v) – v cos(u) and u(r,y) = r² – ry² v(r, y) = y – r Find af af and both by…

A: We need to find the derivatives using direct substitution and by chain rule . Now , we have ,…

Q: Q)is a) x^2=y^3 reflexive antisymmetric Transitive  Explain it correctly,solve only when know…

A: We have to find the correct option