If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). - at

Q: 2)( L[ (1 – 27)' sin 2r.dr)) =

A: Using the formula

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Q: (7) 3x-7>11 ans./ (-co, -4/3) u (6, co)

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

Q: 26. / cor' u du = cor? и - In | sin ul + с

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Q: Assume that f and g are harmonic functions in R^n. Show that div(f ∇g − g∇f ) = 0.

A: Ans- We can start by computing the divergence of the vector field F = f∇g - g∇f:

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Q: Hiw/ Find F'(x) 1. if F(x) = x, tanx 2-if y = Sinx it casx 3- Find g" ()if y co) = Sec y ex) g ex)…

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Q: six 3x sin B. Sin³ x + sinx+c Csix 3 x sinx D.six x + A B C

A: We will solve the problem

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A: We have to prove L.H.S = R.H.S

Q: a) Use the Euler formula, e¹⁰ (cos(0) + i sin(0))" = cos(n) + i sin(n). b) Suppose y(t) = e-2t eit…

A: In this question, we will find the solution to the given problem.

Q: +x- âu ду

A: ∂z∂u=∂z∂x*∂x∂u+∂z∂y*∂y∂u∂z∂v=∂z∂x*∂x∂v+∂z∂y*∂y∂vx=eucoxvy=eusinv

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A: Given equation is: xy2+x tan y=y sin x We have to find dydx.

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point (6,0)? A y = x -…

A: Given, The equation of the curve ey+cosx = 1 We have to find the equation of the line tangent at the…

Q: (b) If f (x, y) = y sin2x + x°cosy °cosy 3 then verify dxðy dyðx

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Q: cos2x a) -.dx,b) xe*. dy Į sin2x. [In(sin2x)]² + sin2x 0.

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Q: Q/ ind dy if 24-sini' (xe!)=sin'(x*)+ cos (x")

A: Given that      2y - sin-1(x2+1) = sin2(x4) + cos2(x4) Here we have to find dy/dx.

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A: Given,

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A: Ans is. option a)

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Q: cos ax -dx = te' 2 х* +1 ле",а 20.

A: In this context, prove ∫-∞∞cos axx2+1dx=πe-a,a≥0. Consider, ∫cfzdz=∫-∞∞cos…

Q: Suppose that 4x² + 2y² = t² and y=tsin 0. Find ду (27) ət 0 and at ?x

A: The given equation is y=t sin θ. Consider sin θ is a constant term.

Q: Calculate F'(0), where 3z2 – (8z° + 3z®") + 10z F(x) = 226 27° – 212 – 10 Hint: Do not calculate…

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Q: Prove that sin? 0 – sin* 0 = cos? 0 – cos* 0. cos“ 0.

A: We can use the trigonometric identity, sin2θ+cos2θ=1 sin2θ=1-cos2θ.

Q: 1/2 yee? +4 dy +17y=0 dx2 when Pove then ydy that Sinzx, %3D0 dx

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Q: B. Let ulr,e) = r"sin(ne). Find 4 2n-2 +u -nr Ure or

A: Given

Q: Show that fi (x) = cos x , f2(x) = cos 2x are orthogonal on [-7,71]. %3D

A: This is a application of integration problem

Q: 2. y" +4y= sin2x + x2 using inverse operator method

A: