Take the Laplace transform of the following initial value problem and solve for X(s) = L{x(t)}: 2" — 2 — 24г — S(t), 2(0) — 0, 2"(0) — 0, where S 1, 0

Q: b) Determine the pdf of Y = ln X (fy (y)), using a transformation method used in this course. In…

A: X~Gamma(ɑ,β)

Q: Prove that for a constant function f(t)= C, the Laplace transform can be given as. F(s)= Z C= S

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Q: Let A(x) = 4 3 2 1 y f(t) dt for f(x) in the following figure. y = f(x) 1 2 3 4 Calculate A(0.5),…

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Q: (d) Let y(x) = [tan-¹ (√)]4. Find y'.

A:

Q: limh→0 -2 0 √2+h-√√2 h 2 represents the derivative of f(x) = √ at x = a. What is a? a cannot be…

A: Given,Given derivative of f(x) at x=a is,

Q: Given function G(x)= 3√2t² - 2 dt. Which V one of the following is true? A) G(3) <G'(3) <G"(3) B)…

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Q: Find Lf 0- £{[ e-axdx } by transforming e atu(t) then applying the integratiori property

A: Given :I=∫0te-axdx Laplace Transform u(t)→ℒu(t)us=∫0∞e-stu(t)dt we need to find: ℒ∫0te-axdx

Q: Consider the following piecewise-defined function: 2, tIn4 (a) Sketch the graph of f(t) and clearly…

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Q: The following picture is the graph of the function y = f(t). 1 1/2 Consider g(x): = / f (t)dt. Find…

A: 2a) From x=0 to x=1 there is a triangle of base=1 and height =1  So we have to find the area of the…

Q: What is the smallest number that can be represented as the sum of four positive squares (not…

A: Consider the given statement. Since we need to find a number, which is the smallest number of sum of…

Q: Find an equation of the tangent to the curve f(x) = √√x+8 that has slope 4 O A. O B. O C. D. 1 y =…

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Q: |The graph of ах + b f(x) = (т — 1)(» — 4) has a horizontal tangent line at (2, –1). Find a and b.

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Q: -> (6) 금 AxB) at t-1 at t=1 (1) A X 4P

A:

Q: Let g'(x) 0. B. g(1) = - 3, g(7) = 1, g(15) = 10 1 C. g(1) = 1, g(7) = 7, g(15) = 14 D. g(1) = 10,…

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