1. If u(x, y, z) find = 21 v(x, y, z) Jºu əx³əy² əzª x³y³ 25 and ე10 əx¹ Əy¹ əz² and w(x, y, z) Jw əx²əyəz = y³√2x² - 325

Q: 6. Solve for x, XE C: a) x³-7x+6=0 b) 2x³ + x²-8x-4 = 0 c) 9z³-4z=0

A: As per the guidelines of bartleby First three question from multiple Parts is answered at a time,…

Q: dx 19) u = 4x + 9 4x +9 1 A) B) 2/4x + 9 + C + C + 9)3/2 1 + C V4x + 9 C) 2- S dx 20) u == 4x + 6 4x…

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Q: 2) Show that 2m +1 m P(x) m +1 -xP (x) m+1 (x)F

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Q: If (1 – i) x + (1 + i) y = 1 - 3i, then (x, y) =

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Q: If U = xz - x²2y + y²z², evaluate div grad U O2y + 2z²+2y² O -2y + 2z²-2y² O2y-2z²+2y² O2y + 2z²-2y²

A: I have given the answer in the next step. Hope you understand that

Q: Solue the guen equaitions %3D

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Q: 2) x + xy+y -7= 0, (1,2) Ans. -4/5

A: We have, X^2 + xy + y^2 - 7 = 0 Differentiate with respect to x, we get 2x + [ x • dy/dx + y • dx/dx…

Q: If r(x, y,z) = (x² + y² + z²)!/2, find a²f a²f əx²'əy² ' a²f , аnd дхду

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Q: 9) Solve: (x + y)dy-(z-y)dx=0 a) x² + y² = C b) z² + 2xy + y² = C c) z²-2ry+y²=C d) z²-2ry-y²=C

A: We need to solve D.E.

Q: a2u a2u 2y дхду a²u )Find du where ax - - axây' ay? u = x3 - 2x2 + 2y3 – 6xy + y ax2

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Q: Vx3y P(x,y) is equivalent to 3x Vy P(x,y). True O False

A: Given that ∀x∃y Px,y is equivalent to ∃x∀y Px,y. To find that the statement is true or false.…

Q: 7. f(2) = -3, g(2) = 2, f2) = 4, g(2) = -5 a) If h = 0, use the values above to find h) 9(x)

A: 7. f2=-3, g2=2, f'2=4, g'2=-5

Q: (a) A = [í 21 B = R s c= D= -2 -5. 4 = G ) B= = L, ) = 5[ -3 -5 (b) A = [; ) B =[ D = 5 -11. -5]

A: Givena)A=2112, B=-30-2-5 , C=-2-402, D=0000.b)A=1114, B=-3-50-11 ,C=19-110 , D=-55-20-25To find All…

Q: Determine Cif u=v=0 (20 — 5и + 3)dv — (20 + 4и — 6)du %3D 0

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Q: Suppose that u × v = ⟨1,0,4⟩. Find (2u−3v) × v.

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Q: If u = eª₁x+₂y+a, where a₁, a2, a3 are constants and 2² u J² u 2² u + = U. a² + a² + a² = 1. Show…

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Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: Given the graph of the hyperbola choose its only correct implict equation below. 8 (-2, 6) 6. (2, 6)…

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Q: If a-(1/a)=b, b-(1/b)=c, c-(1/c)=a then abc=?

A: Given  a-1a=b....(1) b-1b=c....(2) c-1c=a....(3) We have to find abc

Q: then the ² u - y² is მყ2

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Q: у" — бу" + 11у' — бу — 4sin7х + 5 - %3D -

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Q: Use the equations to find əz Әх əz ду II - - əz Әх az Әх and =1 . OF Әх OF az and дz ду 5yz + 3x…

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Q: 2. State the leading coefficient, degree, and symmetry. [K/U 6] b) y= e a) y=3x-4x² + 2 -6x c) d)…

A: Given: a) y=3x4-4x2+2Leading coefficient=3, degree=4 and symmetry=y-axis

Q: 1. Given the algebraic function x² xy + y² = 3

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Q: 18. Define I(a, b) = ª exp(-a²u²_b²u^²) du for a, b>0. Show that (a) 1(a, b) = a¹1(1, ab), (c) 1(a,…

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Q: Let V be an F vector space of dimension n. Prove that, for k≤n the vectors V₁, V2, …, Vk are…

A: A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1+x2v2+···+xkvk=0…

Q: The area between two infinite flat parallel sheets which are placed 10mm away from each other is…

A: Given data :                       The distance between  plate and sheet is y = 4 mm.…