(2) Using Fourier transforms, solve the integral equation for f(x), 1 1 -a|x| - e- -b|x| = L / e-blul f (x - u)du, b 1 -e a where a and b are positive parameters.

Q: Find the constants a and b such that the complex function f(z) = x² + ay² - 2xy + bx²i − y²i + 2xyi,…

A: A function f(z)=u+iv is analytic if ∂u∂x =∂v∂y and ∂u∂y =-∂v∂xGiven…

Q: Jo 8-7. Find the derivative of the functions: (a) h(x) = | In(t) dt g(x) = [" (c) dz 24 +1 3r (b)…

A: Solution: The objective is to find the derivative of the given function

Q: Consider the data about f(x) and its derivatives given below. rƒ(x) ƒ'(x) ƒ"(x) 0 1 14 -1 5 8 6 Let…

A: Given Information:Nodes of  are provided as .The function values and its derivatives are provided…

Q: 4. Perform the indicated multiplication of the two differential operators: (D –x)(x²D– 2x).

A:

Q: (4)Evaluate the definite integral (a)(1+ si 0 1+ sin x)dx (b) (2t+cost) di (b) f( -x/2 x+ X - dx R/4…

A: Explanation of the answer is as follows

Q: Question 27 Determine the second derivative of 6 y - xy2= 1 A y " = 2y³ ( 6 – 2 x y ) -2 ( 2 – x y (…

A:

Q: lim tanx i. x→ 0 lim In(1+ x)] 11. x→ 0 lim sin ax i1. where a and b are constants. r0sinbxr

A: We are only allow to to do first question and three subpart of question So if you need rest of…

Q: Find the Fourier integral of f(x) = e-k* when x>0 and f(-x) = f(x), hence prove that cos(wx) dw w…

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Q: 8) Consider the function f(z) given by f(2)= 24-2 cos 20z² + 1. (a) Show that f(z) has zeros at eie,…

A:

Q: 23. Integrate: S x+2 dx 2 A. V1– x² + Sin-1x + C C. -V1– x² +Sin-1x + C B.V1 – x2 +Sin-1x + C D. –V1…

A:

Q: Match the differential equation with the appropriate slope field. y' = \ OA) B) |||||IVAA -411111 Y…

A:

Q: Consider the following. F(x) = dt (a) Integrate to find F as a function of x. F(x) = (b) Demonstrate…

A: Second fundamental theorem : Suppose f is continuous function in an open interval I .Let a∈I and a…

Q: 4. Evaluate each definite integral using the Fundamental Theorem of Calculus. (c) / (cos r – V3sin…

A:

Q: Find Solution of Homogeneous linear ODE s (D°, 60 +131 Jy

A:

Q: 3. a) Find the Fourier transform of g(x) given that g(x) = 3e¬4|x+2| b) Using the formulas for…

A:

Q: Performing iterations on (25) respectively, leads to the following: n-1 X2km+j v; II n-1 Y2km+j…

A: Given: 2km+j=2km+j2+rj To find: Corresponding equation

Q: (ex, if 0 a 3 Represent the function f(x) = { as Fourier cosine integral.

A:

Q: (a) Determine the domain of analyticity for f(z) = Log(-iz-1+7i). %3D Compute f'(2), f'(7 +2i),…

A: The function is not analytic when the expression inside the bracket is zero.  Thus, get the region…

Q: (b) Prove that sint -dt > 0 t+1 for all a > 0.

A: Given:- ∫0x sintt+1dt >0

Q: [8] Find the complex Fourier integral representation of f(x) = e2x 0 |x| < 1, |x ≥ 1.

A: The given problem is to find the complex Fourier integral representation of the given function.

Q: (a) Determine

A:

Q: 07/ Express in the form x + jy (1) e'(x/2-j) (2) In(3 – j) (3) sin(r/4+ j2) -

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Q: Find the function f(a) such that f'(x) = 5 sinh(x) – 2 and f(0) = 4. a) O f(x) =-5 cosh(x) – 2 z - 1…

A: Given that f'(x)=5sinh(x)-2 and f(0)=4 To find the function f(x)

Q: 3. Prove or disprove: there exist rational numbers a and b such that a/b is irrational.

A: Suppose there exist rational numbers a and b such that a/b is irrational.

Q: Orthogonal Properties of Legendre's Polynomials: L, Pm (x) P(x) dx 2 2n +1

A: