G(u, w) 3 sin (uи) at the point (7, +). Use symbolic notation and fractions where needed. Enter your answer using u-, w-, z-coordinates.)

Q: nction 'a' is 1+eaz at its pole

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Q: U= Sin/x-Y Show that +9u -tanu. 2.

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Q: Prove the identity. cosx sin (x+y) – sinx cos (x+y) = sin y %3D

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Q: Verify the identity: sin(x - y)/(cos x cos y) + sin(y - z)/(cos y cos z) + sin(z - x)/ (cos z cos x…

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Q: tan z, + tanz, = T-(tan z;) +(tan 72) tan(z, +2) ) Prove that: cos(z + w) = cosz cosw + sinz sin w

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Q: sinh (iz) = i sinz sintiz) =isinh z,escia)= cosh: 2. !!

A: In this question, the concept of a trigonometric function is applied, Trigonometric Function The…

Q: ropriate substitution, n³ (4x)cos*(4x)dx is equal to

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Q: how that u(x, y) is harmonic in some domain and find a harmonic njugate v(x, y) hen: u(x, y) = 2x –…

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Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

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Q: Prove the identity cos(x+y)cos y +sin(x+ y)siny =cos x

A: We have to prove the identity                              cosx+ycosy+sinx+ysiny=cosx

Q: 3. u, = u, - sin x cos t, 1 >0 В.С.: и(0, г) %3D0, = () 1.С.: «(х, 0) %3D 0, u,(x. 0) = 0

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Q: f(z) = 3 sin I+ 3 cos z, а (-п, и) on

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Q: 2. Verify the identity: csc(a) = } sec² (4) cot(;) 2 2

A: Given

Q: cos(2z) dz c = |Z| = 1 Evaluate where at oriented 5-4 cos(z) counterclockwise?

A: Let fz=cos2z5-4cosz Singularities of f are those points where the denominator is zero. So, put…

Q: Check by differentiation that y = 2 cos t + 6 sin t is a solution to y"+y= 0 by finding the terms in…

A: Here,  y=2cost+6sint

Q: If F(x,y,z)=sin(x³y²)+cos (Vxy2)+x®y²z, then fyz(1,-2,1)=

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Q: eiz-e-iz 1. Show that Sin z 2i

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Q: San What is the integrable form of sin-cos-sin0 de? 2 2 1- u? du 2 2 cosu du - Ju2-1 du -2 sinu du

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Q: Exercises 1) Find if z = 3 cos x – sin(xy),x = ,y = 3t -

A: The given equation is; z = 3 cosx - sin(xy) , x=1/t , y=3t

Q: (a) x, = a+bZ, +cZ,- • (b) x, = Z, cos(ct)+Z-1 sin(ct). (c) x, = Z,Z, •

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Q: ome If y tanx, prove that y"-2(y +1)(3y+1). ir If x= sect and an

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Q: 2. Using trigonometric substitution, what is f- vx²-9 dx ?

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Q: Compute the Jacobian at the indicated point. G(r, t) = (r sin (t), r – cos (t)), (r, t) = ( 6,…

A: Jacobian of the function at a given point

Q: 1. z, =1-j2 and Z,=2+j3; Evaluate cos[Z,J?

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: Value of a(u, v) is, if u = x + y², v = y and x = r cos 0, y =r sin 0 a(r, 0) 2 xr -2x r2 2x2 r -2x…

A: Explanation of the answer is as follows

Q: **(sec! I tan /)i + (tan /)j (2 sın cos r)k di tan 7)j 50. sec i tan 7)i 0.

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Q: 5. Determine if u and v are orthogonal u = (cos, sin 0,-1); v = (sin 0.- cos 0,0)

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Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

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Q: Let z=x+iy be a complex number such that coshz #0. Then Re(tanhz) is equal to

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Q: 2- Prove that: sin(z + w) = sin z cos w + cos z sin w %3D

A: sin(z+w) = sinz cosw + cosz sinw R.H.S  By multiplying 2 from numerator and denominator 1/2 (2sinz…

Q: Solve 2 sin (z) – sin(z) = 1 over the interval (0, 2) O z= O z= 5, O z= ,, 2'6

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Q: Prove the identity.   cosh(x+y) = cosh x cosh y +cosh x cosh y

A: Given information: coshx We know that, coshx=ex+e-x2sinhx=ex-e-x2

Q: Let r(t) (sin(4t), cos(41), sin(4f) cos(81)). Find the point where r(t) intersects the xy-plane on…

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

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Q: If y= tan x , prove that y`= 2(1+ y² )(3+ y²).

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Q: Compute the Jacobian at the indicated point. (5. 증) G(r, t) = (r sin (t), r – cos (t)), (r, t) = -…

A: Jacobian of the function

Q: Evaluate: sin z dz +(°z – z)

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Q: Prove that ²-1 (²) (0) (sin (+,-) + do r² sin(0)

A: Given : ∇2=∂2∂x2+∂2∂y2+∂2∂z2 To Prove : ∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2 sin2θ∂2∂ϕ2

Q: O IT 3 tan'z sec z dx

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Q: • Find a harmonic conjugate of u(r, y) = x² – 2x – y². Show that u(r, y) = e" cos y is harmonic.

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Q: 4. Verify that the functions 1, r, cos r and sinr form a funda- mental set of solutions of y(4) + y"…

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Q: Let w- fx.y.) - :), x- cos(), y sin(» and :. Then:

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Q: Prove that sinh z = sinh x cos y +i cosh r sin y.

A: To prove, sinh z = sinh x * cos y + i cosh x * sin y

Q: 9. Use the Residues Theorem to calculate 1+ sin² ª -de. Sketch the contour you used.

A: We have to find integral using Residue Theorem.

Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

Q: Prove that: Z,Z2 =r,r2[cos(0, + 02) + i sin(0, + 02)] 1.

A: NOTE- As we are allowed to answer one question in one session so, i have answered first one for you.…

Q: #3, Find tん Xナメy form in Siri (끌)

A: We have given siniπ2 We have to write this in x+iy form As we know sinhz=-isiniz Then,…

Q: +z/3 + sin z dz

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Q: Let = (sin x cos y, cos I sin y, In z).- Compute div i %3D

A: Given,          v→ =  sinxcosy , cosxsiny , lnz

Q: Integrate the trig identity 2 cos j x cos kx = cos(j + k )x + cos(j -k )x to show that cos j x is…

A: