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

Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: Let u = Al 2 [R and v= find a and b such that au + bv [:] 3

A:

Q: A fair coin is tossed two times independently. Let H₁ = {1₁ (1, if head is obtained at the ith toss…

A: When head is obtained at 1st toss then H1= 1  When head is not obtained at 1st toss then  H1= 0 When…

Q: Prove that if Xn X and Ync, then (Xn, Yn) → (X, c).

A: Please see the answer innext step

Q: and B =

A: (2/5,1/5,1/2)

Q: Q.3) Find the constants a, b, c, d, e if f(z) = (ax³ + bxy² + 3x² + cy² + x) + i(dx²y - 2y³ +exy +…

A: Given :  f(z) = ax3+bxy2+3x2+cy2+x + idx2y-2y3+exy+y  is analytic. To find : The constants a, b, c,…

Q: Let X and Y be iid N(1,3). Let U = 4X + Y and V V_dependent or independent? Justify your answer. 2X…

A: Given X  and Y be iid with N(1,3). Mean, μ=1 Standard deviation, σ=3  U = 4X + Y and V = 2X — 3Y

Q: Find d = gcd (270, 105) and hence find integers x , y such that d = 270x +105y .

A: GCD stands for greatest common divisor for two or more numbers.

Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: S 1.Prove that L (coswt): %| s2 +w2

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Q: Q.Show that λ=a+d/2

A:

Q: /| (9x + y – 2z) dS. Is Evaluate S: z = x + 0 < x< 4, 0 <y< 7

A: Given: ∫∫S9x+y-2zdSS:z=x+y2, 0≤x≤4, 0≤y≤7

Q: Let T = x²y-xy³ +2; x=rcos0, y=rsin 0. Find and OT at or 20 TAT

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Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: If R= [0.1] x [0, 1]. calculate In[(x + 1)(y + 1)]dA. 0 B. 2ln 4-2 C. O D. 1 A. In 4+2 B. 2ln 4-2

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Q: 3y², Compute divà and curlà for à = (x²y²z?)î – (2xy² – 16x)ĵ + (9_)&.

A:

Q: Let u= 31-2j + k and v= 2i – 2j + 2k. Find ux y.

A:

Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^.…

Q: O from the equation z = In(x² + y²) + Zyy Show that zxx %3D

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Q: Let I = S (8x + 10y + 4+ 12xy) dA where R = [0, 1] × [1,2]. R Find I

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Q: Let y = 7 and U-span(u), with u = x1 = x2 = -21 TT -4. Write y=x1 + x2, where x1 in U and x2 in U+.…

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Q: Find B so that BH B = A where A is from (1).

A:

Q: (b) Let z = x + iy = re?". Find |z| and z² first in terms of x and y and then in terms of r and 0.…

A: Given:

Q: Find the dual of x 1 + (y + z).0

A: ANSWER IS AS BELOW:

Q: Evaluate L/(x - 2y + z) dS. S: z = 6, x² + y2 < 1

A:

Q: E. Let 2-(e-e(3). Shn that Zy-4(xe ye")=2.

A: