Let u = (1, 2, 3), v = (2, 2, −1), and w = (4, 0, −4).Find z, where 3u − 4z = w.

Q: Express dw/ðr and ðw/ðs in terms of r and s if w = z² + y°, x =r – s, y=r +8.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: f(æ, y, z) = æ²y+ 2y²z+ 3æz?. Compute fa: (1, 1, 1). None of these. 3

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Q: F(x, y,z)= (4xyz) î + (-2xz+2yz) ĵ -3y² z k , find VxF

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Q: Express ∂w/∂r and ∂w/∂s in terms of r and s if w = x2 + y2, x = r - s, y = r + s.

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Q: (b) If z r+ry- y7, 1= u+ and y = 2uv, find: in terms of du %3D u and v.

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Q: F= [y°, 2², x²], C : r= [3cost, 3sint. 2t], 0 < t < 4n

A: Given that F=y2, z2, x2 and the curve, C, such that, r=3cost, 3sint, 2t for, 0≤t≤4π. Differentiating…

Q: Find ∂ w/∂ x at the point (x, y, z) = (2, -1, 1) if w = x2 + y2 + z2, z3 - xy + yz + y3 = 1, and x…

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i + 2j − k, v = i + j + 2k

A: Given vectors are (a)

Q: Find for w = , x = 0', y =r+ 0, z = r – 0 2r2 27 2r 272

A: Given query is to find the derivative.

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 5u − 2x = 3v + w

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Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

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Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3u + 2x = w − v

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Q: Find Duf at P. f(x,y,z)=4x^3y^3z^3;  P(1,−2,1);  u=13i+23j−23k

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Q: Complete the proof that ZYXZ SUT. P Q R. U W Y

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i − j, v = j + k

A: Given: Two vectors are . In part (a) Find the vector product of two vector u and v. therefore the…

Q: Let u(x, t) be the solution of n. и = xt, -00 0, .2 ди (x, 0) = 0, –00 < x < ∞. u (х, 0) - %3| -…

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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: Let f(r, y) = (3 – y)". Then %3D drdy drðydr

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Q: Find r, y, z and t where 6. + 2t 4 r+y 3 %3D -1 2 +t

A: Given  3 xyzt = x6-12t + 4x+yz+t3 We have to find x, y, z and t.

Q: Find Cx(x,y) if Cx(x,y) = 2x2 + 7xy - 9y2 + 4x - 9y - 6 Cx(x,y) = ?

A: Let's find.

Q: If f(z) = z² − (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

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Q: If r = (2x − x²y)i + (3xz − y²)j − (4xy² + x²z²)k, find ∂r/∂x , ∂r/∂y , ∂r/∂z

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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: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: Show that A Yk= V' Yk+r

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Q: f({x, y))) for all c e R and all (x, y) E R?

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Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 2x − u + 3v + w = 0

A: Given u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). And 2x-u+3v+w=0 Plugging the values,…

Q: Be z = (x-y)/(x+y), where x = (u/v), y = (v2/u), calculate ∂z/∂u and ∂z/∂v

A: The given equation is z=x-yx+y where, x=uv, y=v2u. Find the value of ∂z∂u and ∂z∂v. Here we use the…

Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: solve for w where u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v w=?

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Q: Solve for w, where u = (1, −1, 0, 1) and v = (0, 2, 3, −1). 1/2w = 2u + 3v

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Q: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

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Q: Find dw/dr and dw/dΘ for w=2z/y-3x if x=3Θ+2r, y=3r^2 + Θ, and z =4r-Θ, where Θ = 2 and r = 5.

A: w=2zy-3xx=3θ+2r,y=3r2+θ, z =4r-θTo find ∂w∂r and ∂w∂θ for θ=2 and r=5

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: Given f(x, y) = – 5x + 6xy° + 3y, find - fa(z, y) = %3D f,(z, y) = !!

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Q: Fx, y, z) = (10y – az – 5x)i + (3by – x + 8z)k + (z – 5y + 2cx)j %3D a

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Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3x + 2u − v + 2w = 0

A: The given vectors are Let the vector x be

Q: Let u = 2i−j+3k, v = 3i+j−k, and w = 3i+j+2k. Verify Equation (3).

A: Given- u=2i-j+3k,v=3i+j-k and w=3i+j+2k To verify- The equation u×v·w=u·v×w

Q: If f(x,y,z)=exp(3x)cos(-4yz), find Vf. %3D

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Q: Let f(r, y) = 2ry +3x?y2, then fry

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Q: Given f(x, y, z) = V5x – 5y + 2z, find fa(x, y, z) =| %3D fy(x, y, z) = f-(x, y, z) =|

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Q: Find z and z, Zy. z = 2x*y5 !! %3D Zy %3D × | > N

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = 2i + k, v = i + 3k

A: Given that, the two vectors u = 2i + k, v = i + 3k To find the following (a) u × v, (b) v × u, and…

Q: If z = u2 v3 w4 , u = t2 , v = 5t − 8 and w = t3 + t, find dz/dt

A: Given,           z = u2v3w4 , u = t2 , v = 5t − 8 and w = t3 + t

Q: Find r'(t), r"(t), r'(t) · r"(t),

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.