Find the divergence of U = r cos 0 a, - sin 0 ag + 2r² sin 0 2 sin 0 3 sin 0 - r2 2 cos 0 3 cos 0 r2 2 cos 0 3 cos 0 - r 3 cos(03r2) 2 cos 0 r2 r2

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A: To check the given solution satisfy the given partial differential equation, substitute the solution…

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Q: 6. (a) Recall that sin z = ¹2; cos z = (i) Find real and imaginary parts of sin z and cos z, for z =…

A: Note : '' As per guidelines we will solve first three subparts. If you want any specific subpart to…

Q: 2) f(t) = 4t3 sin %3D

A: we have to find Laplace transform

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A: Given equation is  x3y'''+3x2y''+xy'+8y=xlnx            (i) Let x=et. Then…

Q: z cos(2x)) - cos(2x))+

A: here using sin2x = 2sinxcosx                 cos2x = 2cos^(2) x -1

Q: sin adx =? O A. - cos r + 2 Cos cos z | +e 4. O B.-z+2-증 O C. - cos x +2 cos I +C COS D. cos x cos 2…

A: Given: I=∫sin5xdx We know that sin2x=1-cos2x                                              ..1 So, by…

Q: Find the general solution of (4) **" + 16y " – 8y'– 17y =0 y * + 8 y given that r1 = -4 + li is a…

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Q: e cosl – i e™ sin 1 + e¯ cos 1 - i e- sin 1 2 e cosl + i e™ sin 1 – e- cos 1 + i e¯I sin 1 -TT 2 e…

A: Simplify the given expression: Coshπ-i

Q: -2 cos(6t) dt J (10+4 sin(6t))²

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Q: Evaluate and simplify aluse yuotent rule to Rind US. dxL3x t. / Find. d dx [sec(cos/(1 JCX

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Q: xux-yuy+y2u=y2x find the general solution

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Q: 8z Find where z = 4 sin(xy), z = te58, and y= 105-1088 dt O O O O dz = 4(10t5-10s8) cos(te5s…

A: We have to find  using given data.Concept required:If  then while finding we will consider  as a…

Q: Y 4 1.2) ["se sec ¹ √e de e 20) ff 2² 1 x² ln x dx

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Q: =} = (² S +4)² = cos t} = se

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Q: Given, y = (1+ cos 2t)-Find dy dt 8 sin 2t (1+cos 2t) sin 2t 5 (1+cos 2t) -4 sin 2t 5 (1+cos 2t) 8…

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Q: Question 9 Find tan'r sec?t dt A - tan²t+C B tun't + C tan" Isec*t +C_ an*r+C 4 D

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Q: X₁. (x₁, Yr) (x', y') 0 (x, y) X x' = x + (x-x, )cos-(y-y,)sin y' = y, + (x-x) sin 0+(y-y,) cos P' =…

A: Solution:

Q: QU/A Find the domain and range for the following finctions: 1- y =Vx?-6 2- y = QI/B Prove that 1+…

A: Explanation of the answer is as follows

Q: L (sin? t) What is f (t), f' (t) and f (0) ? O b) O a) f (t) = sin t, f' (t) = 2 cost, f (0) = 0 f…

A: We will find out the required solution.

Q: v (t) x w (t)=((t)i + (sin t)j + (cos t)k) x ((3t)i + 2k) ijk t sint cos t 3t 02 =(2 sin t)i + (3t…

A: The cross product of two vectors A and B is given by:A=ax i +ay j +az kB=bx i +by j +bz…

Q: fze [sin(3x)]-m(x, y, z), where m(x, y, z) = Part C. yz-1 %3D

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Q: Implicit DiffeYentia tion Find dy if +Sin xy Find dy if 2X- 3y=8 Use implicit differentiation to…

A: We have to differentiate the given expression.

Q: Use implicit differentiation to find dy/dx. 18) y cos = 4x + 4y - y sin A)- cos B) sin 4y 4y2 D)-…

A: 18.we have y cos(1y) =4x+4y⇒dydx(cos(1y) )+ysin(1y)×1y2dydx…

Q: /Prove that the value of cos()dz, when z = T + 2i is e + e-1

A: Complex integration of the function

Q: sin'r dr

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