1. Use mathematical induction to prove а) 1 - 1! + 2- 2! + ... + n:n! 3D (п +1)! — 1 for all n 2 1.

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A: We have to apply the partial derivatives.

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A: Please find step by step solution below:

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Q: 13 14 6 8 -1 13 2 5 16 11 9 Example 4.4. Using the partition method, find the inverse of A = 7 3 9.

A: We need to use partition method to find an inverse of matrix A.

Q: 3. Which of the following is always true for any real nur O For real ɛ > 0, if x-yl s &, then x = y…

A: 3. For 1st option: let  x = y + ∈ then |x-y| ≤ ∈ but  x ≠ y So option 1 is incorrect. For 2nd…

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Q: 2. Determine the volume generated about y-4 the area boun ded bay ×キの x and x?ty =3 メ %3D

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A: Sol

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Q: ANBANBA' O B A'N B'

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A: Given series is ∑n=2∞(x+46)n2ln(n)

Q: Use Induction to prove that 22n+1 + 32n+1 is divisible by 5 for all n > 0.

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Q: what is a maximum spanning tree And give examples

A: The given question is related with graph theory. We have to define maximum spanning tree. Also we…

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Q: Question 5 Let a and b be positive real numbers and 6+ 1. Find a+6 if the exponential function f(x)…

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Q: 1 and let A = -2 3 be the 5 9. Let v = and v, = 3 matrix for T : R? R relative to the basis B = {v1,…

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Q: find the total dominating set for: Kmin

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Q: 6. Suppose f :Z→Z is defined as f = {(x,4x +5):x € Z}. State the domain, codomain and range of f.…

A: From the definition of a function it follows that ℤ is the domain and codomain of f.

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Q: 1. Which of the following is false? * O If x > 0, then 1/x > 0. O If x > 1, then x^2 > x. O Ifx< y,…

A: We have to find the correct option from the given options.

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Q: a, = -2a,-1 + 24a,-2 for n > 2 with initial conditions ao = 3, a = 4. The solution is of the form:…

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Q: 50 107 36 A = 25 54 20 31 66 21

A: This is a problem from linear transformation.

Q: Proof of CRT (for two moduli) We must prove that f: Zm,ma Zmx Zm gimern by is a bijection.

A: We shall solve this using various properties of GCD. The detailed typeset solution is presented in…

Q: x' – y = 0 у — 2 — у %3D 0 2(0) %3 2, у(0) %3 1.

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Q: x' = -3x + 2y, y' = -3x + 4y; x (0) = 0, y(0) = 2 %3D %3D

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