Problem 2. (a) Use the long division algorithm to divide x³ +5x+3 by 3x+2 in Z/7Z.

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A: Given,           y''-10y'+9y=e-9t; y(0)=1, y'(0)=1

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Q: Express the limit as a definite integral on the given interval. n lim [² cos Xi X₁ Ax, [3π, 5π] 318…

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A: Given that An isosceles trapezoid RSTU, as given in fig.

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A: We use integral by parts to solve the given problem.

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Q: Question 4 (a) Show that V(x, y) = ln(1 + a²) + y² is a Lyapunov function for the system x² x' (t)=…

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Q: b) A unit vector is a vector whose magnitude is unity, given that the vectors r₁=2i+4j-5k and r₂…

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Q: 2. Let T: R³ R³ be the linear transformation given by x1 + x2 + x3 +((:))-[ T X2 2x1 x2 + 7x3 -4x₁ +…

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Q: 5. [-/15 Points] DETAILS ZILLDIFFEQMODAP11 7.3.033. MY NOTES ASK YOUR TEACHER A 4-pound weight…

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Q: Given: function f(x) with dom f = R \ {-1} lim_ f(x) =- 00, lim f(x) =+ 00, lim [f(x)-(1-x)] = 0,…

A: We know,f'(x) = 0  critical pointif  f'(a) =0 and  f'(x) &gt; 0 for x &lt; a and f'(x) &lt; 0 for x…

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Q: Sketch the graph of f with emphasis on concavity. Label asymptotes with their equations and…

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Q: QUESTION 1. Consider the following data X 4 5 6 7 0.6 .65 0.74 0.78 Use forward difference formula…

A: We use Newton forward difference formula to solve the given problem.

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