Calculations. For each sequence, explain whether it is conver- gent, divergent to t∞, or otherwise divergent (not to ±x). If it is convergent, find its limit. 3 n→∞ 2-ni (a) lim (b) lim x-2 x²4 x + 4

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A: To Do:We have to solve the system

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A: We are using partial fraction to find inverse Laplace of given functions.

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A: The path of particles:

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Q: 7. Let G be a finite semigroup. Prove that there exists e E G such that e = e².

A: is a finite semigroup.

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A: The vector is: .To Find: magnitude and angle.

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A: Definition

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Q: 4: state and prove L is a normed space ?

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A: Find the general solution by computing complementary function and perticular integral.

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Q: Round off 2553 N to three significant figures in KN

A: First we will convert 2553 N to kN.