Let w = r = uv, s = u – 2v. Use appropriate forms of the p2+ s2" dw dw and du chain rule to find in terms of u and v. du

Q: Solve for w where u = (0, 1, 1, –1) and v = (3, 0, –1, 2). %3D w + 2v = -4u W =

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Q: Find the following

A: Given, ∫5z+2dz To solve the above integration.

Q: Differentiate. x3 7) y = X- 1

A: Given : y = x3x-1

Q: Find Hhe (imet 3. 3. im +y²+xy

A: Explanation of the answer is as follows

Q: Verify that (AB)T = BTAT.

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Q: 4. Calculate fx J₂ dx

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Q: Let C z-1=3 and1 = §, = dz. Then

A: The solution is given as

Q: Find all values of x so that u · u = 50, where

A: Given u·u=x34.

Q: Find the dim U where -3 4 U = Span 1 -9

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Q: дz If z = f (x, y), find and for the following equation ду дz дх

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Q: Draw the function y = x^2 + 2x %3D

A: Since, it is a second degree polynomial in x, it is called a Quadratic polynomial which has two…

Q: дz дz \f z = f (x, y), find and for the following equation ?х ду z = (x2 + xy3)4

A: Let Using the chain rule, and

Q: Let i = (– 3, - 2, 3) and i = (1, – 6, – 7). Compute the following: i xü = i x ủ u X u =

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: Calculate for w = xyz. By

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Q: xyzx + 2y³ (Zyy) = 1 Dependent variable/s: Independent variable/s: Type: Order: Degree: Linearity:

A: Given: Here, the dependent variable is z, independent variables are x and y. And the type is a…

Q: For which values of ß does {(1,0, ß),(1,2,–3)(B,1,0)} span R'?

A: If spans the same subset of R³, the vectors must be linearly dependent to each other.    Therefore,…

Q: State Fubini’s theorem.

A: Statement of Fubini's theorem

Q: () Let z = x + iy. Find Im and Im 2 in terms of x and y. Im Im z2 ||

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Q: дz дz If z = f(x, y), find a and for the following equation əx ду z = x² + 3xy + y³

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Q: Find YI if YI =x - 5 and YV= x – 4 Y \I V Z.

A: We will find the solution in the following step

Q: 2. fote-t² dt

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Q: let R = (-2, 7). Calculate the following: The components of u = PŔ, where P = (1, 2)

A: Given,               R=(-2, 7)   and   P= (1, 2).    The components  of u=PR⇀=?

Q: Vxdx 2. For J T-Vx use 4 O u = JA u = x O u = Ja

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Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

Q: Express E: livenr coumbination of Ÿ; = and V as a

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Q: Find // VdA, + 1 R -dA, R= [0,3] × [−1,1]

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Q: Soly

A: Given  u = ( -1 , 0, 1, 1)   v = ( 2, 3, -1, 0)

Q: Find the value of x x - 2 x - 1

A: claim- find the value of x

Q: Compute the Jacobian for the substitutions x = ρsinφcosϴ,  y = ρsinφsinϴ,  z = ρcosϴ.

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Q: Differentiate the function. u' +71

A: Topic = Derivative