Show that the series Show that the series N=1 Cos N is divergent. E Σ (cos N)/N² is convergent. N=1

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A: We recall the binomial theorem for fractional index.

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Q: -xX 2) y"+2y+y = xe

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Q: Simplify first then evaluate: a. log5 625 + log2 32 b. log4 √64 C. log₂ 160 - log₂ 5

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Q: There are TWO (2) questions. Answer ALL questions. QUESTION 1 Apply Newton's method to solve the…

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Q: Find both eigenvalues A₁ and A₂ and corresponding eigenvectors X₁ and X₂ of the matrix A= You MUST…

A: The given matrix is The characteristic equation of A is

Q: fn = = 2 n²+n−1 3n2-10

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Q: Consider this system of equations: X1 - X2 X3 1 x1 - x2 + x3 = 5 -x1 + x₂ + x3 = -6 A. Write the…

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Q: State the inverse of each relation Given the ordered pairs: ((3,-2) (-1, 5) (4, 0)} the inverse…

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Q: Solve the initial value problem y' = and find the interval of the maximal solution. = y² + 2xy x²…

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Q: In P2, find the the standard basis C = {1,t,t²}. Then find the B-coordinate vector for 1 - 2t + 2t².…

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Q: Identify the graph of h(x)=4(x+4)2+6. Then identify t

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Q: Find the maximum value of the following function: f(x, y, z)=z- x - y - x² - y² - z² - - XZ.

A: Given information:A function .To find:The maximum value of the function .Concept used:To find the…

Q: Simplify the following expressions in the indicated polynomial rings: A. (3x³ + 2x² + 4x + 2) + (2x¹…

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Q: 7. In the given equation, find the value of x X (³27)² = (-²) ₁

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Q: Find the midpoint of the line segment joining the points P₁ and P2- P₁ = (d,n) P₂ = (0,0)

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Q: 1. Simplify by using exponent rules. Answers must only have positive exponents. a. 3 -8 -2 FrP 0.5…

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Q: Consider the set S composed of the points on the line segment S₁ between points (-1,0) and (2,0) and…

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A: From the given information above we have a sum of 54 and 27 is 81.

Q: 2) Solve the equation y' = Y 4x²y + x

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Q: Using the ordered pairs definition of the integers ℤ, verify the distributive property for ℤ. (You…

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Q: Prove following… S = 12k for integer k , T = 4p for integer p Prove that S is a subset of T

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Q: Find the general solutions in powers of x and state the recurrence relation: (2 - x2)y" - xy' + 16y…

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Q: How to find the answer? I have give u the right answer. The congruence 3x^2+4x-30=0 has • 2 in Z15,…

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Q: Let X be a set with exactly n elements, where n ≥ 2, and consider the group P(X) with the symmetric…

A: The question you provided is related to concepts from abstract algebra and set theory. Here are the…

Q: the Graph the inverse for each relation below (put your answer on the same graph). -4-3-2 CON -3 2 +…

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Q: 1/ [1¹8 in Evaluate the integral 7¹8 In t dt

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Q: 9. Suppose a population of 250 crickets doubles in size every 6 months. How many crickets will there…

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Q: 2. Suppose DCR and functions f: DR and g: DR. Suppose to is an accumulation point of D and lim f(x)…

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Q: d² y dx² 2 −9y=x, y(0) = 0, y'(0) = 5

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Q: 9. 10. Solve log, 8 1 64 a. Solve log(3x + 1) = 5 a. 1 43 b. -16 b. 8 C. C. -64 300 d. 4 d. 33333

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Q: Exercise 8.9.1 Find the algebraic and geometric multiplicity of each eigenvalue of the following…

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Q: Exercise 8.11.2 I know a certain real 2 x 2-matrix A. My matrix has complex eigenvalue λ = 1+2i and…

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Q: Calculate the measure of kurtosis (group data) x = 97.5 s = 14.47 Class Limits 69-77 78-86 87-95 96…

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Q: When y² = 1+x 1- y² error by 21 order Runge-Kutta method at initial condition of y(2)=3, what is the…

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Q: Assume that T is a linear transformation. Find the standard matrix of T. T: R² →R¹, T (e₁) = (3, 1,…

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Q: Using the priority list T2, T3, T7, T6, T₁, T4, T5, schedule the project below with two processors.…

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Q: Find the laplace transform of the following function f(t) = 58(t-7)

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Q: 1. IfT: R² R³ is a linear transformation such that T(e₁) = (1,-1,3) and T(e₂) = (5,-2,7) where e₁ =…

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Q: Give a formal proof of the following argument. exercise PS2.10 (AB) A V B

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Q: 6. Let v₁ = 4 3 generated by {V₁, V₂, V3). V₂ = 8 [81 V3 = 6 5. [10] and u = 2. Deteremine if u is…

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Q: T T T T T T F F F F F F F For all sets AN Q = A For all sets A, if AN q = A, then you are the pope.…

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Q: Write this function as a step function fe-(t-1) 0≤t 1 X3

A: A step function  can be written in the form:for all real numbers x.If n ≥ 0, αi are real numbers and…