QUESTION 4 Using the definition of convolution find the convolution of the following functions (f*g) f(t) = {2; −1≤t≤1 Otherwise g(t) = u(t)e-t

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A: Note: Hi thank you for your question. As per the guidelines we are solving the first question as…

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A: What is your table? Use the formula and properties of laplace transform we solve the problem.

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Q: Match the slope fields shown below with the differential equations 1. y = 4-y 2. y' = y² 3. y = y 4.…

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A: Here the solution for q(x) and r(x) in Z7[x] are  q(x)=5x2+2x+1r(x)=6

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A: We find distinct eigenvalues and their corresponding eigenvectors.

Q: 3. Evaluate: (i) x¹8¹; (ii) 8,8/8/ (iii) 8¹,8

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Q: A matrix of order n is diagonalizable if and only if A has n distinct eigenvalues. True False

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Q: Test the convergence of the following series 2. Σn=0(-1)+1 (n!) ² (2n)!

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Q: Use separation of

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Q: What is the general solution of the following ODE * (x² + xy - y²) dx + (1²/7 -(x² - 2xy) dy = 0

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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: dP/dt + 2tP = P + 6t - 6 a) Find the general solution of the given differential equation. b) Give…

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Q: g (t) 3, 05. 10₁ 5 ≤ + √ 8 A 8 >

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Q: 1. What is the equation of the axis of symmetry for the parabola with the equation y = - 2 ( x − 3 )…

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A: Option b is correct.

Q: ii. iii. iv. Prove that "if n is an integer and 3n+ 2 is even, then n is even" using a) proof by…

A: According to our guidelines we can answer only one question and rest can be reposted.