2. (a) Let X = y and %3D 0 5 -3 2 8 X 3. Find X. 3. (b) if A = 0 sin(a) 1 then find all the values of a in (0. 27] for which A is invertible 0 1//2 1 (Hint: Compute first det(A)). 522

Q: -1 < x <0 The Fourier integral of f(x) = 1, 0<x<1 0, otherwise 00 (1 – cos(w)) sin(wx) dw lw 1. 00…

A: Given that fx=-1-1&lt;x&lt;010&lt;x&lt;10otherwise The Fourier integral of f(x) defined on -∞,∞ is…

Q: 0 0 0 1 0 0 0 1 0 ) Let A =

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Q: Compute L(f(t)) 13. L((t+1)²) 1. L(2t) 14. L((t+2)²) 2. L(4t) 15. L(t(t+1)) 3. L(1+2t + t²) 16.…

A: In the given question wen have to find the Laplace transformation of the given functions. here we…

Q: By the odd extension method applied to the function f(x)=e-2=, where r > 0, the Fourier integral of…

A: Given function fx=e−2x where, x&gt;0 We have to find the Fourier integral by the odd extension…

Q: 64. Use the finite Fourier cosine transform to solve the heat conduction problem t> 0, 0 0, where…

A:

Q: 2. If :|S1, determine the maximum modulus f(:) (a) f(=) =z-2z+3, (b) f(=) == +z-1, (c) f(=)3= :+1…

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Q: Suppose an undamped forced spring mass system is driven by the equation + 9x = f(t), dt where the…

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Q: 7. By using the Fourier transform, find a solution for the following problem (P Ju(1, x) = 4u.z(t,…

A: The complete solutions are given below

Q: 4.) Suppose X has moment generating function MX(t) = 0.3e−t + 0.1 + 0.1et + 0.2e2t + 0.3e3t. What is…

A: It is an important part of statistics. It is widely used.

Q: 2(3) Calculate the following commutators: (a) [d/dx, x·d/dx] (b) [sin(x), cos(x)] (c) [x^2, Ĥ] ,…

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Q: [2.73 Find a general Solution of following monhomogeneous limear 1ogeneous linear ODE g+ +1+#)は = e…

A: non-homogeneous differential equations

Q: A homogeneous string is stretched and its ends are at x = 0 and x 1. Motion is started by displacing…

A: The boundary conditions are y(0,t) = y(l,t) = 0 and initial conditions are y(x,0) = μ0sinπxl and…

Q: 2. The inverse Laplace Transform of the function F(s) = 4s+2 / s²+2s+5 is : (a) e* cos 2t + 2e* sin…

A: Given function is Fs=4s+2s2+2s+5

Q: 1. Use the Laplace transform to solve the following given initial-value problems. a) y'+y=8e", y(0)…

A: As per the guidelines I am supposed to do the first question among multiple questions. To get the…

Q: Pls help ASAP

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Q: 3. Find the residues of the functions 1- cosz а.) b.) c.) z'e at z=0; .5 e -1 and express the types…

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Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

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Q: 4. Use Laplace transforms to solve the following initial value problems. d?x dx (a) +2 +4x = 0 ,…

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Q: 1 Let H(s) Using convolution to find h(t) s2 (s-a)

A: Inverse Laplace transferom

Q: Suppose an undamped forced spring mass system is driven by the equation + 9x = f(t), dt where the…

A:

Q: 3.17 Use Laplace transforms to find the solution to the follow ing set of equations dt dy2 42 +…

A: Set of equations given as,

Q: 1. Show that the field F = (x + cos a)i+ (K +4 – y sin y)j + (2³ + K – 9)k is conservative and find…

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Q: 2) If g(x) = dt then g'(x) • (1+ 2t)' 3 -1 (a) (1 + 2x)* * (b) +e (d) (1+2x)ž +e (1+ 2x)³ (1+2x)à *…

A: As per our guidelines, we are allowed to answer the first question only please resubmit other…

Q: B. Switch the order of integration: cos (x2) dædy. Just SET UP with the order switched. DO NOT…

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Q: 8. Use the Laplace transform to solve the given initial-value problems. у" - 2у'+2у%3Dsinf, y(0) 3…

A: Given differential equation is  y"-2y'+2y = sin(t) , y(0) = 0, y'(0) = 0.

Q: 2. Evaluate ř(t) dt: 4 4t ř(t) t2 + 5t + 6' î + 2e4t cos t j - k; a = 0 and b = 4 t2 + 1

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Q: SSS zdV Q3: Evaluate E + y² + z² = 1 and x² + y² + z² = 4 in the upper where E lies between the…

A: We have to evaluate the integral ∭EzdV, where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4…

Q: 1. (a) Solve the following equations by using Laplace transform; i.) d?x/dt² + 4 dx/dt + 3x = 2 x(0)…

A: Given

Q: 4. Use Laplace transforms to solve the following initial value problems. (a) y"+2y-3y = 10 sinh 2t,…

A: Laplace transform.

Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: 6. The energy stored 'W' in an inductor is given by (t2 - 21 -2t dt W =

A: The solution are next step

Q: 6. Suppose f(2) is analytic in |2| 1, and f(0) = 1, f(0) = 2, compute: %3D (1) h = fe(s+ 1)2d: (2)…

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Q: 0= "D = °P 0.1 4. b = Sf()sin(n@,t) dt=: 4 |(30t-3)sin(5nzt )dt 0.4 30t - 3 : sin(5nnt) cos5nnt 30…

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Q: 4. Use Laplace Transforms to solve the following initial value problem (IVP): y"(t) + y(t) = f(t),…

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Q: |1) Use a sine expansion to compute the solution of ( ди д'и at ôx? u(0,t)=u(1,t) = 0,t > 0, u(x,0)…

A: According to the given information, it is required to compute the solution of the given equations.

Q: 1.Suppose that the joint p.d.f. of Y, and Y, is defined by: e-Y1/y2 · e-Y2 0 < y1 < 0, Y2 0 < y2 < ∞…

A: Given: The joint p.d.f of Y1 and Y2 is defined by:

Q: Show that the p.d.f. of Z is given by g1(r) = e-1(+A)cosh(vAx), x > 0, where cosh(2) = }(e² +e=*) is…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: メ1+ x€ Lat F Cx, x = F•dr whera yer CIS elosed c is Sagmants from C0,3) to Co,0) than from C3,0) to…

A: Given F=yexyi +xexyjand path is closed

Q: Find the Wronskian for y, = sin 3x , and y2 = cos 3x.

A: The Wronskian, W, of two functions, f and g is calculated as follows. W=fgf'g' , where, f' , g'are…

Q: Prove that by Gamma Function eit + e' e-st dt 2 s2 + 1

A: We will find out the required result using Gramma function.

Q: Suppose w = In(æ² + y² + z²) , Compute dw/du and dw/dv in two different ways: ue3" sin(9v) , y :…

A: GIvenw=ln(x2+y2+z2) where x=ue3vsin(9v) , y=ue3vcos9v and z=ue3vTo find∂w∂u and ∂w∂v

Q: 1- Find dwi dt at the given value for w ==+2,x = cos (1), y = sin (1),z = w =-+ at = 3

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Q: Suppose w=x/y+y/z, where x=e^(4t), y=2+sin⁡(4t), and z=2+cos⁡(3t). A ) Use the chain rule to find…

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Q: min ||y – Hx|3 + A ||x||3 x = (H'H + AI)-1H'y (18) In reference to (18), why is HTH+ AI with A > 0…

A: Given - minx y - Hx22 + λx22 ⇒ x = HTH + λI-1HTy           18 To find - In reference to (18), why is…

Q: Prove that by Gamma Function pit +e e-st dt %3D s2 +1

A: Gamma Function: The gamma function, denoted by is denoted by which is convergent for Some…

Q: 1-6 Use an appropriate form of the chain rule to find dz/dt. 1. z = 3x²y*; x = r^, y = r² 2. z =…

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Q: 1. On (–1,1), two functions Y1 (x) = e2« cos x, y2(x) = e2ª sin x are linearly independent linearly…

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

Q: 2) For a random variable X, its kth-order moment is defined as E(X*). Given the p.d.f. fx(x) of X,…

A: Given, for a random variable X, its kth order moment is defined as EXk and its Fourier transform…