Find the curl of 7 = pz² cos þap + z sin² þ az.

Q: Determine the fifth roots of z = (4-j5)cos(1+j3). Express your answer in rectangular form

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Q: z = tan¯1(4 – j7)

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Q: Prove that eax (a cos bx +b sin bx) + C. ax cos bxdx %3D a2 + b2

A: ∫eaxcosbxdx=eaxacosbx+bsinbxa2+b2+C

Q: Inside one loop of the lemniscate r2 = 4 sin 2u

A: Given:The equation of lemniscate is: r2=4sin2u. To find: The area inside one loop.

Q: фаф, If B = r sin @a, - r² cos pap, a) b) π find B at (2,3), 22 convert B to Cartesian coordinates

A: Given that

Q: Let z=x+ iy with x and y are real. What is the imaginary part of sin (x + iy)

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Q: Let the position vcctor bc R CE) = <3€,2 cos (3€), 2 sin (3€) Compute the curuature

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Q: Express as a product. sin 4ẞ + sin 10ẞ + sin 22ẞ + sin 16ẞ

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Q: Where are the theta valuss for the horizontal and vertical tangent lines on [0,2pi) of r=1+cos theta

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Q: (sinhz)(coth’z+csch*r)dz

A: Integration is done.

Q: Find all x and y between O and 27 so that the equation is true. cosx+i siny = sinx+i x = 4 or 4y = 2…

A: Explanation of the answer is as follows

Q: 3. Let R = {(x, y) : 0 < r < L,0 < y < H} and g(r) E L?(0, L). Find the series solution for the…

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Q: Hin Find Fourier trins form of fu) =/! Ixa ! sinp Then find: O :oS Ein Pa Cos px_dp , ☺ dp

A: We have to solve the given problem by Fourier transform.

Q: Again differentiate with sespect do 'x get we A cost- B Sinz A cosz + BSiny) { from @ d +

A: Please refer the attached image for complete solution.

Q: Evaluate ¹ (x²+x²2²)dzdx by using polar coordinates.

A: We have to evaluate the given integral using the polar coordinates. First we have to identify the…

Q: x+y then x +y- ôy If u= cos %3D +.

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Q: Find the slope of the tangent line to the polar curve 7 = 1-sin 40 at 0= 04 0- 12/12 O 5√3+4 1-4√3

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Q: Express as a sum.(cos au)(cos bu)

A: Given : (cos au)(cos bu)

Q: Is 1 sin u sec u TRUE for all values of u? - COs³ U 1 + sin u

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Q: (b) Find the entire length of the cardioid r = a(1+cos0).

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Q: Find cos theta is sin theta = 1/2 and theta terminates in QII

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Q: Əw ər Find when r = 5 and s= -5 if w= (x+y+z)²₁ x=r-s, y = cos (r+s), z = sin (r + s). Əw ər = |r =…

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Q: fex) Cos X ノ

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Q: ) Find the derivetine of the fnchiog h(x) = I sinhex-7x 4

A: h(x)=74sinh(2x)-7x2Differentiate w.r.t…

Q: 9 Prove Sen 4t 4 cos3t sint-sin3t cos t.

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