Question 2: Verify the following: e-as (a) L{u(t – a)} =. F(s) = L{f(t)}. (b) L{f(t – a)u(t – a)} = e-a$ F(s) where

Q: Determine whether the following functions are refined. Show all reasoning. (a) e² (b) Re(z) (c)…

A: Since you have posted a multi subparts question according to guildlines I will solve first…

Q: £/ ue "du +

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Q: (b) Find A fo given that fo = 3, f1 = 12, f2 = 81, f3 = 200, f4 = 100, f5 = 8

A: Forward difference table is given below: x y △y △2y △3y △4y △5y x0 y0 △y0=y1-y0 △2y0=△y1-△y0…

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Q: Evaluate L{f(t)} for t+1, t20, t1, t#2 t=1 t=2 (a) f(t)=3, -3,

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Q: Show that (a) x(t) * 8(t) = x(t)

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Q: -altl Find the F.T. of g(t) = e to aso

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Q: Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = (s > 0) f(t) † (2, 2) 1

A: Handwriting solution

Q: Let Pr[A]=0.6, Pr[B]=0.7, and Pr[A u B]=0.8  find Pr[A/B]

A: From the provided information, Pr[A] = 0.6, Pr[B] = 0.7 and Pr[A Ս B] = 0.8

Q: (a) div (g) = Ag clas div (fDg) = \f • Dg + f Ag Show that

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Q: 2. L{(2t – 2) U(t – 2)} |

A: We have to find Laplace transform of given function using Heaviside Shift Theorem.

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A: (1) For the given curve two possible points for where derivative of f(x) is zero.Concept: A point on…

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 3t5 L{f(t)}

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Q: TT f(c)dc)+ =xtan"(x) 4

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Q: Find the F.T of the following; f(t) = e-jwot %3D

A: Given: f(t)=e-jw0t we can write  f(t)=e-jw0t.1 By using property y(t).e-jw0t→F.T2πδw+w0

Q: Express the following functions in the form u+iv f (2) = In(2)

A: We know that the complex number z=x+iy can be expressed in the form z=r·eiθ where  r = x2+y2 and…

Q: 2 1 ri - 5x3 + 6 = 0

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Q: If L-[F(s)] = f(t), evaluate f(0) given by the expression F(s) : (s+2) %3D s2 (s+1)'

A: Solution

Q: Let V be a vector space. Prove the following cancellation property: If c 0 is a realee and cx = cy,…

A: 2) Let V be a vector space. Prove the cancellation property," If c≠0 is a scalar and cx=cy then x=y"…

Q: Find F(s). F(s) = L{t(et + est 23

A: Solution is uploaded below.

Q: Calculate F(s), if given f(t) the following is b-be cosbt at (5).f(t) =

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Q: Evaluate f(2) for f(t) = 1 + u₂(t)t.

A: Given: f(t)=1+u2(t)t To evaluate: f(2)

Q: Use Theorem 7.1.1 to find {f(t)}. (Write your answer as a function of s.) f(t)= (t+1)3 <{f(t)}

A: The given function is .We need to find its Laplace transformation.We know that the Laplace…

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Q: Find the inverse for the function f(x)=D (x + 3)°. %3D Ox = V3 + y Ox = V3 - y Ox = Vy- 3 Or= Ox =…

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