Find L[f(t)], where: f(t) = { 1, t², 4, if 0 ≤ t < 1, if 1 ≤ t < 2, if t≥ 2.

Q: В. B. Show that the function f (z) = -i z2 is analytic.

A: The solution is given as

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Q: Let f e E(0, ox) and let a be a positive real number. Define the function fa as follows Sal) = {";…

A: Properties of Laplace transformation

Q: of and ду of For the function f(x,y) = In (x+ 3y), find

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Q: 3. Find the domain of the following functions: a.) f(x) = V1-x Inx b.) f(x) = Vx - 1lr

A: solutionsince the given (3)(c)f(x)=1-xlnx(b) f(x)=x-l ln(x)use have to find the domain of the…

Q: 3. (b) Consider the function f(x, y) = a(x² + y²) + xy + 1 for some real number a. Find Vf. Find fxx…

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Q: Consider f(x) = 3|x|, which is in R[-2, 2]. %3D b. Use the function F(x) to find ſ², f.

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Q: Evaluate L{f(t)} for if 0 < t,t + 1,t # 2 if t = 1 1 (i) f(t) = 3 -3 ift = 2 (ii) f(t) = 1 2t +1 if…

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Q: Suppose that f(x,y)= [15x²y ; 0<x<y<1 0; otherwise.

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Q: Let f(x) = 5- x and g(x) 2, find: a. (fog)(0) b. (go f)(0) = c. (fo g)(x) Preview d. (go f)(x) =…

A: Value of the above ques is

Q: Find the general solution to the homogeneous differential equation tion can be written in the form s…

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Q: Let f(x) = x. Show directly that f ∊ R[0, 2]

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Q: Determine where the function f(x) = O A. (-∞, ∞) 1-00 O B. O C. O D. 3 3 3 (-∞0,²21) U ( 212,00) N/W…

A: we have to find out the values of x where function is continuous.

Q: 1 X ƒ (t) dt = 1 – 1 418

A: Given:  ∫1xft dt=1-1x To Find:  To find ft.

Q: 2. Let f(x) = 3x + 6 € Z7[x]. Find all associates of f(x).

A: The given function is fx=3x+6∈ℤ7x To find: the associates of f(x).

Q: Let f(t) = 2t² for -4 < t <4 and extend periodically. Compute: f(1) = f(5) = f(-4.5) = f(-8)= f(12)…

A: Periodic function: A function is said to be periodic with period T if f(x+T)=f(x).

Q: Since f(x) is continuous between a and b, the function needs to cross the x-axis. O TRUE O FALSE O…

A: Given fx is continuous between a and b

Q: The function f(x) = x² + 1 satisfies Rolle's Theorem in the interval [-2, –0.5]. - x² Select one: O…

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Q: Let (a,m) 1 with m>1 and let f = expm (a). Then

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Q: Let S«) = {r²+2x}°, 121, ax+bx, x< 1. Compute for all a and b such that the function f(x) is…

A: We have to find

Q: Let S(x²+2x)², x> 1, f(x) = Tax+ bx², ах x< 1. Compute for all a and b such that the function f(x)…

A: Proceed as shown