Find L{f(t)} using the First Shifting Theorem. Note: a, b, e, w, k and n are constants. 1. -kt 2. L{e (acost+ 6 sin t)}

Q: 5. Let z = and f(z) = 27 ,then simplify f(2) and indicate the real V2 – yi and imaginary part.

A: The given complex number is, z=1-2-yi Rationalize the term,…

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Q: 16. / cot(z) dr 17. cot (x) dr 18. csc(r) dr

A: (16) ∫cot(x)dx ∫cot(x)dx=∫cosxsinxdxPut t=sinx      dt=cosxdx we get-∫cot(x)dx=∫1tdt…

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Q: Consider f : R → R given by f(x) = x². What are the domain, codomain and range of f?

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Q: x+5)(x-2)2 (x-3) Select the Domain of the rational function R(x) a. (-00, -5) U (-5,2) U (2,3) U (3,…

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Q: Let n be a positive integer. Define the function fn(z) by dn dzn Find the value of fn(-1+i).…

A: Solution:Given: Let be a positive integer. the function is defined bywe have to find the value of

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Q: E. Calculus Showthat the difference quotient for f(x) = sin x is given by f(x + h) – f(x) _ sin (x +…

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A: solution of the given problem is below...

Q: Draw the y = sinx and y = 1- x² on the domain -2 <x<2 and filling the between the funtions.

A: the filling part is given below-

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Q: A graph of f (z) =a cos(br) is shown, where b is a positive constant. |(0, 4) (T, 4) |(27, 4) -2…

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Q: Find a harmonic function o on the upper half-plane that takes values ø(x) = 0 for |a| > 1 and $(x) :…

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Q: H.W using differentiation prove that SinX s Cos, व

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Q: The domain of the function f(x, y) = sin¯¹(x + y) is the set of all points in the xy-plane.

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Q: a. f(t) = cos(2t). Find F(s) b. g(t) = e²t sin(3t). Find G(s) c. H(s) = 3s +1 s² - 2s + 5* Find h(t)

A: We have to find the Laplace transform and inverse Laplace transform.

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Q: of of and da For the function f(t,a) = sin (8rt + 7a), find %3D - at

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Q: adf. Let f(z)=3z-2/[(z-2)(z+1) (z-4)]. Howmany simple poles has the function f?.

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Q: Find Duf at P. NOTE: Enter the exact answer. Duf= f(x, y) = sin(3x – 4y); P(4,3); - = u 3 i

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Q: Please solve this problem with a good explanation. It is a linear Algebra  question Thank you.

A: (a) The given f is in V if it satisfies