Problem 8. (i) Prove that curl(u × v) = div(u ® v – v ® u) %3D

Q: 2πT 1 I₂ = So dt. 13 + 5 cost Let I be the unit circle {z e C : |Z| = 1} parametrised in the…

A: Solution:Let z=eιθThen z=cosθ+ιsinθ (By Euler's…

Q: . (Section 14.4) Let curve C be described by vector function(t) = (cost-1, sint, 3/2) on 0 ≤ t ≤ b.…

A: The curve C is defined by the function,on the interval,The length of the curve on the given interval…

Q: 2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j +…

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Q: Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²))j + (3x + 4y +6e²² (a) Find curl F. curl F - (b) What…

A: We will use result of part c  which gives line integral in closed curve and combined it with line…

Q: Find the two roots of (j)'/2 in rectangular. a) 0.770 + j0.770, –0.770 – j0.770 c) 0.707 + j0.707, –…

A: c

Q: If r(t) = = cos(-3t)i + sin(−3t)j – 10tk compute r' (t)= i+ i+ (cos (-3t))/3 and fr(t) dt= (-sin…

A: r(t)=cos(-3t) i+sin(-3t) k-10tk

Q: If the covariant tensor has components in Cartesian coordinates x',x². Find its components in polar…

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Q: Let i be the unit imaginary number. Thus i2 = -1. (1) Observe that the usual algebra rule to…

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Q: Let sin(4x + 7y°) x3 + y5 if (x, y) # (0,0) f(x, y) = 0. if (x, y) = (0,0) %3D Which of the…

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Q: | Let r(t) = 5i + t²j – t²k. Compute the unit tangent vector T(t) at time Question 7. t = 1. 5 (a)…

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Q: The indicial equation of (-1) y"+ (-1)y'+2u 0 at r=1 is: (A) + 2r +1=0 (B) r1 2r = 0 (C) r-r= 0 (D)…

A: Given differential equation is (x-1)2y"+(x3-1)y'+2y = 0

Q: 3.8. Question. Match equations y' = sin x, y' = cos y, y' = y cos(x)· a) c) b) to direction fields.…

A: To find the direction field of a differential equation you first need to isolate y' from the…

Q: Problem. Consider the helix R(t) = cos(2t)î + sin(2t)ĵ + 4tk (a) Compute R'(t) and R"(t) (b) Compute…

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Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: Solve for the higher order DE number 2

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Q: Find Fourierexpansion of the Punction fcx) = x2 XE [-T, TT] then deduce thetn = | 2' (572 (7)2t. (2)…

A: Since you have asked multiple questions, we will solve the first Question for you. If you want any…

Q: 3. Triangle DEF with vertices D(0, 6). E(3.5), and F(1, 1): 90° counterclockwise about the point…

A: Rotation is a rule of transformation. Through this transformation, one can produce a new image by…

Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

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Q: daffəx and åf/ðy y) = x² – xy + y² v) = sin? (x – 3y)

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Q: Calculate the imaginary part of  ∮C(Re(z)+3.43)(1z^2+9z+11 / z)dz  where C:|z|=1  Use FOUR…

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Q: (a) What is the maximum directional derivative of g(x, y) = y²e2¤ at (2, – 1) and in the direction…

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Q: Prove that a parametric function given by I= 21 + 312 y = t² + 21 satisfies the equation dy + 2 dr…

A: see the details solution in below

Q: у" + 4y' + Зу %3D sin (e*)

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Q: -2x Use Green's Theorem to evaluate [(3 ye^²* − 7 sin² (3x³)) dx + (5x² + 2x²y² +8e³¹²-7x+²) +2) dy…

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Q: (ii) e*u + e'u„ = u XX yy

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Q: A' C 2. B C' B'X 0 2 4 6 ? . 8.

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Q: Calculate x +y - z in degrees. [Image 18 1 B (z- 15) (22) D

A: calculate x + y - z

Q: Find the general solution to the hypergeometric ODE #(1 – 2)y" + (; - 2-) a - - 0. 3 ) y y = 0.

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