1) Prove the following identity: (x + y)² – (x – y)² = 4xy

Q: 1. sin xsin ydx+cos x cos ydy = 0 2. dr = b(cos Odr+rsin Ode) 3. x cos² ydx + tan ydy = 0

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 10. y = C, cos 4x + C2 sin 4x + C3xcos 4x + C4xsin x + C5; C, to C5 are arbitrary constants

A: Since their are 5 arbitrary constants so the differential Equations will be of order 5. We find the…

Q: If y = cos ¹ prove Zyy + z = 0. )Z = (1 + i)(2-1)-¹, find |Z|.

A: Here given y=cos-1(z/x). We prove that zyy+z=0.

Q: If x=sin@,y=0 ,y=cosp0,Prove that (1-x²)y,-xy,+p°y=0

A: Given, x=sinθy=cospθ Required to prove, 1-x2y2-xy1+p2y=0...1 Then finding dydx by using chain rule,…

Q: Show that the following gn are harmonic and find its conjugate u=3x^2y+2x^2_y^3_2y^2

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Q: If y = exp(-x²) show that -2xy and hence prove that, for n > 1, %3D y(n+1) + 2xy(") + 2ny("-1) = 0.…

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Q: (b) The For any X1,...X, and Y1,..., Ym, we have: n п т Cov EXi, -ΣΣCον (X, Y) i=1 j=1 i=1_j=1 Hint:…

A: From the property of covariance,  Assume that X and Y are the random variables. Therefore,  CovX,…

Q: Q53- X--) (xij-Xi - X.j+X)=Zero 13D 「に )に prove that e to

A: We need to prove the given equation.

Q: 2- Exercise: Evaluate a) L{4x2 – 3 cos(2x) +5e*} b) L{4+ sin (x) – e** } -

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Q: If x, y and z are independent variables and f(x, y, z) = x sin(y + 3z) of then find ôz .

A: Here, x,y,z are independent variables. Given function is f(x,y,z)=xsin(y+3z)

Q: d csc 'x dx -1 Prove that xVx? – 1 2.

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Q: The identity LiS L xyzdzdxdy = "/2 S Sa rsin@cose zdzdrd® x² +y² 1-y² x² +y² is

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Q: 7) Suppose a is a positive constant less than 7. Prove that the equation 2r+cos r = a has a real…

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Q: 21. Let h(x) = tan(5x + 6). Then %3D h'(2) is and h"(2) is

A: 21) The given function is: h(x)=tan(5x+6) To find h'(2) and h''(2)

Q: 1. how that { cos(Inx), sin(Inx)} is a fundamental solutions set for x²y" + xy' + y = 0 on the…

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Q: S eln (1-t) 1-t - dt ed to you in any form

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Q: 6. y = C, cos x + C2 sin x + C3 cos 3x + C4 sin 4x ; C1, C2, C3 and C4 are arbitrary constants

A: The given equation is, y=C1 cos x+C2 sin x+ C3cos 3x+C4sin 4x Differentiate this equation up to the…

Q: 3.(1) Show that (x) - J{«) )x cos 2.x

A: Consider the Bessel function, Jnx=xn2n Γn+11-x222n+2+x42·42n+22n+4-…             ...1 Substitute…

Q: HW klx) = 2x+5 ㄱ 1. Find ke-¹(x) 2. Prove by kokorklok

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Q: 3 .4 D² + 2D+4 ak* sin 3x}

A: We have to solve given problem:

Q: 1 Assume that 1 < a < b_and equation is solvable. + x = Show that this * – b'

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Q: Solve for the following z-transforms: XIn] = u(n) - (0.6)" un) b.) x[n] = 10 sin (0.25 ñn) un)

A: By Bartleby policy I have to solve only first one as these are unrelated problems.These are…

Q: ー19- EX: Fined the sd. of he l-U.2 っ24 ニ4 224 る2 ノ メ424 u())こCos(メ424) + cs(x~て47 ] +出 「d. メー24

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Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

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Q: Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

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Q: Prove that x² = 13 (1²) + 1) = (xin(e))) ১0 sin(0)

A: Given  x=rsinθ cosϕy=rsinθsinϕz=rcosθ To prove :∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2sin2ϕ∂2∂ϕ2

Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: 7/2 79. Prove that 0< sin x dx < Ja/4

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Q: 28. IfI:zxzr = 0, ris a. positive b. negative с. zero d. impossible to determine from the…

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

Q: 2ху 3. y' = -x?

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Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

A: The given differential equation is  y'=1+sin2xy On simplifying this, y'2=1+sin2xy. Hence the…

Q: If y = exp(-x²) show that = -2xy and hence prove that, for n > 1, y(n+1) + 2xy(") + 2ny(n-1) = 0.…

A: Given that : y=e-x2. Therefore,  dydx=ddxe-x2=e-x2.-2x=-2xy  , as y=e-x2. Hence proved that…

Q: (B)JE w = x*+y+z° and x = PSin ø cos@ »y=pSing Sino and z- Pcoseo prove that -2P Cos 2Ø and' %3D

A: Given  w=x2+y2-z2x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ

Q: Ôz Ôz If Z= tan"'(2) -= 0 show that : *-+ y ôx ôy

A: Let us consider function z=f(x,y) Where f is function of x,y. ∂z∂x represents partial derivative of…

Q: az az and ду Ql:- Find the if Z = x4 sin x y³. Əx

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Q: - Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and…

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Q: -1 If cos x+cos y+cos z= T, prove that x +y +z +2xyz = 1

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Q: Express Q(x) = cos4 (x )+ 12 as the composition of three func-tions; that is, identify f, g, and h…

A: Q(x) = cos4 (x )+ 12 We need to express the given function as a composition of three functions  that…

Q: 4.3 Use the calculus of residues to evaluate the following integral 2m 1 de. 1+8 cos? 0

A: We find the given integral by using calculus of residue.

Q: In AXY Z, the mZY = 90°.XY = 19 and XZ = 22. What is cos X? ООО О

A: Given,

Q: 4. Use the first Fundamental Theorem of Calculus to find 3r 2-1 dt 12 +1 sin 2z

A: Fundamental theorem of calculus Let us consider the continuous function f(x)  on the interval [a,b]…

Q: 4.3 Use the calculus of residues to evaluate the following integral 2 1 1+8 cos? 0

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Q: Let f(r, y, z) = In(x² + 2) + y?e - cos(2y2). Find feyr-.

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Q: Can i get help step by step?

A: Given integral is WE will use following substitution to evaluate the integral

Q: 1. If y= tan x, prove that y= 2(y´ +1)(3y² +1).

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: 3. 1+x2 хр xp q Find b such that J Tuy2

A: By using integration formula we can find the value of 'b'. See attached for detailed solution.