Find Wr 0 if W = f(x,y) x=r cos 0 and y = r sin 0, then prove that r Wr 0 =yfx + xfy + xy(fyy-fxx) + (x² - y²) fxy

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Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: fyx if f(x, y) = sin(xy) + x² In y cos(xy)- xysin(xy) - cos(xy) + xysin(xy) + cos(xy) – xysin(xy) +…

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Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

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A: Given: W=spanℝ1, cos2x, sin2x=ℝ+ℝ cos2x+ℝ sin2xWe need to justify for each given subsets that it is…

Q: Find fy if f(x, y) = sin 5x cos 5y O fy = 5sin 5x sin 5y fx = cos 5x cos 5y O fx = 5cos 5y cos 5x fx…

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Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: Find nd cos(z ² + y²)dA where D = {(x, y) | 16 ≤ x² + y² ≤ 81} D

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Q: What is the B of f(x, y) = tan (x3³+ 2xy)? [sec ² (x²y³+ 2xy] (3x²y² +2x) [sec² (x²y³ + 2xy ] (+²+*+…

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Q: Exercise: Find dy O y = lox +3 Cost ® y =cscx- 4 Vx +7 Cotx 1+ Cotx

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

Q: (ysin x+xy cos x)dx+(xsin x+1)dy = 0 Ans. xy sin x+ y = c

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Q: Let C be a constant. Consider Compute(a) da. ان | دن 3 7 3 73 ㅠ + CT 53 + СT 7 + СT 3 -x², f(x) 2) =…

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Q: of of +y y Let f(x, y) = x$y² tan Then x equals X

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Q: u(x, y) = -e sin x - 2e* siny. Find a harmonic conjugate v of u, namely a function v such that the…

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Q: What is the A B (C) D af - of f (x, y) = tan (x²y³ + 2xy)? dy [ sec 2 (x2y3 + 2xy (2 xy + 2y) 2 [sec…

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Q: | | | 8. Given f(x) = sin (4x + 7/7), find f' (Z). a) 0 b) 4 9. The derivative of y = √√ex is: a)…

A: Step 1: Step 2: Step 3: Step 4:

Q: By, Where F(2, y, z) = sin yi+(2 cos y+cos z)?+y sinză und (sint, £,2),0 < t < 2

A: Value of the line integral

Q: x = s·t u = x² + y³ +z*, {y = s² +² z = s- t

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Q: ) Find the directions in which the directional derivative of f (x,y) =4x2+sin (5 xy) at (1,0) has…

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

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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: on f(z) = e cos x+ ie-Y sin x is entire.

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Q: [The following initial value problem is defined with an exact differential equation. If the solution…

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Q: Knowledge/Understanding Multiple Choice: [ 1. Derivative of f(x) = cos²x a) 2cosx 2. Derivative of…

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Q: Compute the dz in the function z = ety sin (xy) A. dz = ze"(cos (zy) + sin (ry) dz+ ye"lcos (ry) +…

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Q: Abstract Algebra: Assist me please.

A: To prove that the kernel of a group homomorphism is always a normal subgroup of the domain (group)

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Q: of the following function: ду Find the W = COS (x2 + 2 y) - e4x – z*y + y3

A: The given function is w=cosx2+2y-e4x-z4y+y3.

Q: -2n f) S“ cos 2x dx g) S et² t dt h) S x sin(x²) dx

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