In Exercises 47-50, verify that wy Wyx- 48. w e+ x In y + y Inx

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A: To evaluate the integral,  ∫tanxsec4xdx Rewrite the term sec4x=sec2x·sec2x…

Q: In Exercises 47-50, verify that Wy %3D Wex- 47. w In (2x + 3y) 48. w = e + x In y + y Inx

A: NOTE-  As per our guidelines we have to solve only first question. Given data- w = ln ( 2x + 3y ).…

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A: Given,           If W-10, 4, X-3, -1, and Y-5, 11 of ∆WXY.

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

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Q: 1 Using Convolution theorem, find (i) L (s+a)(s+b),

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Q: a²z If z = In(x² + y²)., find ax2 ay?

A: Here we have;  z=ln(x2+y2) ...................(1) partial derivative with respect to x

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A: Solution:

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A: Given statement is false.

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A: In the given partial differential equation with the given initial condition. 4ux+uy=u2u(x,0)=11+x2

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A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

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Q: Let X,X2, ,X, be a ranc *(X), = 0*(1– 0)1-x; %3D

A: from above distribution is binomial  f(x)θ=θx(1-θ)1-x  ;0&lt;x&lt;1 E(x)= nθvar(x)=nθ(1-θ)…

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Q: az Find if yz – In z = x + y ax 3.

A: We have              yz-lnZ=x+y

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Q: Exercise 2. Prove that if A = B and C z D, then A × C = B x D.

A: Given data: A≈B......(1)C≈D......(2) The objective is to prove A×C=B×D

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: Let F I2). Evaluate JJaw as z² + y? 0

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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

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A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

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A: Formula used: Consider the vector field as Fx,y=Px,y,Qx,y, Then the vector field is conservative if…

Q: In Exercises 23–24, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = 1 + xy2 - 2z2 24. ƒ(x, y, z) = xy + yz…

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Q: 1. If x, y, z E R, prove that (a) \x+y\ < \x| + \yl- (b) |x– y| < |x – z|+|z– y|, and (c) ||지| -…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Fiven with z1 = (-3,1) and z2 = (1, 4). Show that |21 2| = |21||2|- %3D

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Q: b) Verify uxy = Uyx , if u = In /x² + y² . %3D %3D

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A: We have find the jacobian

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A: true please see explanation in step 2

Q: Use Cramer's rule to solve for z. Зх — 4у + z %3D 3 2х + 3у = 8 5y + 8z = 11

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Q: 3. Show that à = (6xy + z³)î + (3x² – z)ĵ + (3xz2 – y)k is irrotational. Find p such that A Vọ.

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Q: Show for all x, y in R |x+ys]xl + ]y!

A: consider left hand side  and use the result x=x2 x+y=x+y2=x2+y2+2xy≤x2+y2+2xy≤x+y2=x+y

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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: Compute the convolution y(n) = x(n) * h(n) , Where x(n) = {1,1,0,1,1} and h(n) = {1,-2,-3,4} , Using…

A: Given: Given convolution expression is Y(n)=x(n)*h(n) x(n)={1,1,0,1,1} h(n)={1,-2,-3,4}