4.w. Fourier series For Exイ fcx). ースくくくo アーメ 0くxくn

Q: use direct Fourier transform formula to prove thès 8o -at t é ut ult)

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Q: /find the Fourier integral representation of the given function. x0 -x le

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Q: 5. Find the Fourier integral of frowl x (•

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Q: To find the Laplace transform of e^(6t)cos(at)you would substitute  into s/(a2+s2) which gives ?…

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Q: Evaluate by using definition Gamma Function 2

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Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

A: Partially differentiate the function with respect to x.…

Q: One solution of a 2nd order homogenous LDE is e2*sinx. What is its general solution?

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Q: The integrand Vx² + 64b², b > 0 , after substitution, becomes: x2 + 64b² %3D

A: Here we replace x by some variable so it makes our integrand easy to solve.

Q: Q3\ Determine the z transforms to the following Z{sinh ka} *

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Q: 37nx Find C2{sin (*} (Finite Cosine transform) O A. 6L O B. 4L - 5TT OC. 2L - 5T O D. O E. None

A: Find C2sin3πxL

Q: Solve the equation (2x + 6) (2y² + 3) dx + 4y(x² + 3x + 2) dy = 0

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Q: Find all real singular points of x(x2 –7 x + 10) y" + sin(x) y' +x y =0. {-6, –6} None {5, 2} {4, 3}…

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Q: Show that given that z = sin-12 дхду дудх

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Q: Provide the General Solution of each differential equations. Box your Final Answer and show your…

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Q: Given: s (s + 3) / (s^2 + 4)(s^2 + 6s + 10) . Express the inverse transform as an integral.

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Q: Q2) Evaluate: So x sin 2x x² +9 .dx.

A: We use the Fourier transform to evaluate the following integral.∫−∞∞xsin⁡(2x)x2+9dx

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

A: Given

Q: a) Compute the quotient (22 + 2i) / (2 + 2i) b) Suppose z = (In 2) + i (pi/2). Compute e^z

A: " Since you have posted two questions, we will solve first question for you. To get another question…

Q: Show that z- sinh z Rcs :* sinh z

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Q: Fourier Series of 2 – on the interval [-, n 2+ 7? -E 1)* sin (n2) 2+ㅠ2 -X, L'co () =D1 8(–1)" cos()…

A: As per Bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: 5.6.3. Let f(x) 16 interpolation points. Then, plot f(x) along with the resulting (real)…

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Q: Prove that • tan'z = —— In ( + + ²/² ) 1-Z

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Q: Q4) Considering fanction of fla)=x, & -ncacrR a) Is this function odd or even b)epand fantion sine…

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