Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

Q: Show complete solution. Expand, that is, perform the indicated operations on the differential…

A: We have to find out the operation

Q: Show that the two linearly independent solutions of xy" – y + xy = 0, x > 0 can %3D be obtained as…

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Q: 1. What should be A for the path independent of (2,4) xy + A 2dy – x y? fip- (1,2) Moreover evaluate…

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Q: Calculate the iterated integral A 67 5x cos y dydx. 1 2n 5

A: Explanation of the answer is as follows

Q: Integrate counterclockwise around C. (Show the det に+1 20. ‚ C: |z − 1| = 3 - ²-iz + 2

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Q: 2. Use the Definition of Residue to show that: dz -ni 3 Jizl=1z² sinh z Where 0 < |z| < T.

A: Image is attached with detailed solution.

Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

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 Fourier Integral for the function: f(x) = {0 x 0 0 <x < 2 1 ans: f(x) = - " sin2w cos(wx) +…

A: Given function fx=0    x&lt;0 or x&gt;01    0&lt;x&lt;2 So we must have  fx=0    x&lt;0 or x&gt;21…

Q: d x"J,(x)=-x"Jns(x) d, n+1 X.

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Q: Evaluate the integral. HINT: 3 x2 dx J2 x - 1

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Q: Assume x and y are functions of t. Evaluate dt for 2xy - 2x + 4y3 = - 56, with the conditions = -…

A: Given      2xy-2x+4y3=-56 →           1      dxdt=-16, x=4, y=-2

Q: A) Show that from the lower relations near the point (0,0,0, 0) u can be written as a derivative…

A: Given relations: vcos(y)+xcos(u)=0 ucos(x)+ycos(v)=0 To find the second order Taylor polynomial of u…

Q: Determine Taylor's formula of order 1 and center a = (0, 0) of f(x)=ex1sin(x2).

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Q: Evaluate the improper intergal 1 dx using the residue (x2 + 9)* theorem.

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Q: Evaluate the improper intergal 1 dx using the residue (x² + 16)² theorem.

A: We need to evaluate integral.

Q: Consider the definite integral. (8x- – 1) e*x²-x dx Let u = 4x2 - x. Use the substitution method to…

A: Answer and explanation is given below

Q: z'sin3z Evaluate dz with C: -2 using Cauchy's integral formula

A: *concept:- Cauchy Integral formula.

Q: Find the local linear approximation of f(x) = In(5 + x) at xo = -4. %3D In(5 + x)

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Q: Show complete solution. Expand, that is, perform the indicated operations on the differential…

A: Given: xD(D+x)

Q: ii) √²√³ xy² S¹S. -dydx -3 x² +1

A: Evaluate the iterated double integral.        ∫01∫-33xy2x2+1dydx

Q: y = sech*x = In(_+ V1- x², sechx = In(- 1+ V1-x² Prove that .... ..

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Q: Evaluate the iterated integral: dydx - 1/4 Jx2

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Q: Evaluate the integral. 5n /2 2, 1 - cos t dt 3π/2

A: ∫3π25π21-cos2tdt=∫3π25π2sin2tdt=∫3π25π2sintdt=∫3π22π-sintdt+∫2π5π2sintdt=1+1=2

Q: Evaluate the integral. 1 cos 2t dt 2 7x/2

A: To evaluate the given integral.

Q: Evaluate the integral 3 2x cos(xy)dydx 2

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Q: 2n Jnsi (x) = " J,(x) – J(4)

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Q: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

A: The function is fx=xyThe region is bounded by y=x, y=6-x, y=0

Q: д. L. = a(x, y)+b(x, y) +c(x, y). – d(x, y) -

A: Proof: Consider V be any vector space of all functions of two variable x  and y whose partial…

Q: nsi Sinhna (na)? 8. ) Sind( x) Sin y)

A: Given Fourier series, ux,y=∑n=1∞1sinhnπ8sinnπ2nπ2sinnπ2sinhnπy2+8nπ2-8cosnπnπ2sinnπx2sinhnπy2 To…

Q: Evaluate the improper intergal dx using the residue 2 (x² + 4)² theorem.

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Q: Let z= 28x + 32xy - 8y , where x(t,s) = cosh (4t) cos (5s) and y(t,s) = sinh (4t) sin (5s). ze at…

A: Here, z=28x2+32xy-8y2

Q: Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

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Q: It u-ys Int, Ya っ 3. to ny find by rusing ypropoiate chain rule

A: Given, Let, u=rs2ln(t), r=x2, s=4y+1, t=xy3

Q: show that f(z)=(z-1) cos(1/z+2) has an essential singularity at z=-2

A: Introduction: Laurent series has an important role in determining the singularities. Suppose, a…

Q: Explain Bessel equation and Prove that 2 (i) (ii) In+3X + Jn+5X =÷(n+ 4)Jn+4x 4J"n = Jn-2 – 2Jn +…

A: Definition Bessel's Equation: The differential equation x2d2ydx2+xdydx+x2-n2y=0 where n is a…

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z2 sinh z Where 0 < |z| < T.

A: Use the following formulae, to evaluate the given complex integral. Let z0 be a pole of order n,…

Q: 2 2. Evaluate the iterated integral 6x'y dady

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Q: (1) Show that F(x, y) : (2x + y, x - y) is path independent and use the fundamental = theorem of…

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Q: Evaluate the in tegral (x+ 2y) dy

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Q: * Lct X; ~ exp (2) · Show that T= EX, is Su fficient pro pesty of T %3D

A: How to find the sufficient statistic 1. Find the likelihood function 2. Apply the Neymann…

Q: find the volue of the od specify ingrol integrol T-x2 the

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Q: Show that {zn}nEN is Cauchy, where z, = sint dt. 1+t

A: Sol

Q: Use the Integral Test to determinOwheher the scrie sure to show that the hypothescs of the Intogr al…

A: Given

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where 0 < |z| < T.

A: Cauchy residue theorem is one of the method to evaluate the integral of analytic functions.…

Q: 4y" – y = 0, У-2) %3D 1, у(-2) %3D -1

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Q: Evaluate the improper intergal 1 dx using the residue (x² + 1)3 theorem.

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Q: (B) Compute div F and curl F for F= x²yi- (z3-3x)j + 4y2k %3D

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Q: Show complete solution Expand, that is, perform the indicated operations on the differential…

A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x