Compute the following. • Arc length of y = (1 + x)² with 1 ≤ x ≤ 4. Area of the surface of revolution generated by the curve x = when rotating it about the y-axis.

Q: 1.-Proof by mathematical induction that 5 + 9 + 13 + ··· + (4n + 1) = n(2n + 3) ...

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Q: Suppose the variance of X is 95. What is the variance of .09X?

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Q: (a) Let F= 2xz2i+j+xy³zk and f(x, y, z) = x²y. Compute the following quantities: (i) Vf (ii) curl(F)…

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Q: 2. Determine the roots of the following function and draw its graph f(x)=x^² - x³ - 16x² + 4x +48

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Q: Can you conclude that A = B if A,B, and C are sets such that A U C = BUC and An C=Bn C?

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Q: 13. Two points, A(3, 5) and B( 2, 7), are joined by vector B. Determine the magnitude and direction…

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Q: Verify that the given differential equation is exact; then solve it. (9x² + 7y²) dx + (14xy+9y²) dy…

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Q: I don't understand this.

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Q: Solve the given differential equation by undetermined coefficients. y'' + 2y' = 2x + 9 - e-2x

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Q: 1 1+e 1 E +3kT-E)/kT 1+e(Ec+3kT-E₁) /KT 1+e 1+e -1 - (E. +3kT-E/KT 1 -(E+3kT-E₁\/kT• e(Ec +3KT-E,…

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Q: Suppose the variance of X is 14. What is the variance of .47X?

A: The objective of this question is to find the variance of a random variable that has been scaled by…