I. Evaluate the following integrals. 1. J 1 - coth² (log₂x) dx x cosh (log₂ x)

Q: estion en Instruction Complete the venn diagram Solve Solve Solve Solve Solve Content A = {4, 5, 20,…

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Q: Using Laplace transforms, solve the initial value problem y" - 2y + 10y = 0, y(0) = -3, y'(0) = 3.

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Q: - 80000 dollars. The group intends to sell

A: Given:C(x)=12x2+500x+8000p(x)=1000-12x Then, TR=p*xTR=(1000-12x)xTR=1000x-12x2

Q: II. Evaluate the following integrals 4. 3² dx S · |e* − e│ + (e* + e) 0

A: Here given integration as I=∫03ex-e+ex+eexdx

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Q: using Laplace transforms y"-2y' +10y = 0, y(0) = -3, y'(0) = 0

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Q: Find the solution of x = X₂ JED -6 where u(t) = 2 and x(0) = [1 -1]. 11 0 JUCE + u(t) (10)

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Q: 1.) Give the Fourier transform of the function f. Sx ha x = [0, 1] f(x) = 0 otherwise.

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Q: F(s) 8Bs - 7C (s + 3)(s - 4) (As − 1)

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Q: 12. Which of the following is submonoid of (Q, *) where a*b = ab? A. (Z, *) C. ({0}, *) B. (R+, *)…

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Q: Question 1: Solve the following differential equations using Laplace transform method. dy a) +7y=5…

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Q: 3 (|3* − 1| + |3* – 3|) dx

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Q: 13 2 1 Given A = 2 13 3, find wwww 4 2 1] the lower triangular matrix. [3 0 0 a. 2-1/3 0 C. [4 −2/3…

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A: This is the question from Linear Transformation.

Q: Obtain the power series solution of the differential equation y"-(1+r)y=0

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Q: The following differential equation is a Bernoulli equation: 2 dy = y² y3 where y = f(t) dt +

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Q: II. Evaluate the following integrals 2x 2. S -dx 2 5+2x+x 2

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Q: Find the inverse of the following matrix 2 3 0 1 4 6 ol

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Q: 13. Which of the following is a subgroup of (R+, *) where a*b = (ab)/2? (Q, *) A. B. (Z, *) C. (Q+,…

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Q: Evaluate J by means of Simpson's rule with n = 2m =20 and h =0.05 J= exp(-x²) dx Answer in 4 decimal…

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Q: Evaluate J by means of trapezoidal rule using n = 10. Round off your answer to the nearest ten…

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Q: 5.x-2y+z=0 2x+y=3z=5 4x - 7y+z=-1

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Q: S ii) Show the DE is not exact (2y²+3x) dx + 2xydy = 0

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Q: (a) Solve the differential equation 1 "+y' + y = 0.

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