z" +7.84x = 5 cos(3t), (0) = r'(0) = 0

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Q: Exercise 10.6. For each of the following, find an integer a realising the congruence. a) 8a 1 (mod…

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Q: Derive the Laplace transform for the given time function: f(t) = eat

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Q: Find the eigenvalues of the given matrix. 16) -49 -97 6) [27090 17) [+49]

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Q: 1. Consider the power series 27² 2"n n=1 a. Write the first three nonzero terms of the power series.…

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Q: 2. (a) Design a bijection between ZU [1, +∞) and (0, +∞). Justify your answer.

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Q: Let a, b, c E N. (a) Prove that if gcd(a, c) = 1 and gcd(b, c) = 1, then gcd(ab, c) = 1. (b) Prove…

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Q: 1 S 1 1 + x² the approximate value of the integral using the trapezoidal rule with n= 3…

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Q: b) f(x, y) = ln(xy) + √x-y + In(62²-52-6) √1-v-2y² d) f(x, y) = √1-y + √1-2² +In(16-2²-4y²)

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Q: Let N R R be any norm on Rn. Show that N is a convex function (give all the details for the proof).

A: Given N :R^n→R be a norm on R^n.      To show : N is a convex.     Definition of norm :…