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Q: one of the More important the orem {n real analysis is faton's Iemmar state the lemma aud say some t...

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Q: If the sum of first n even natural number is 420,find the value of n

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Q: When the median is computed for a sample, all values in the data set are * .used True O False O

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Q: one of themore important theroman real ani llyGes is Fa tou's lemma. state the lemma and say Sometih...

A: In the question , basically asking for Fatou's Lemma and its proof .   Fatou's  Lemma  :  Let {fn}  ...

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A: The complete solutions are given below

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A: The given differential equation is  y'=x3+e10x+7, if y=20.1 and x=0  

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Q: :Q2. Solve the following IVP using Laplace transformation y" + y' + 9y = 0. y(0) = 0.16, y'(0) = 0.

A: Introduction: The Laplace transformation is very much useful to solve a higher-order linear or non-l...

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Q: Determine whether the improper integrals converge or diverge. If possible, determine the value of th...

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Q: Table 5.2.1). . (a) (c) -7/8 dx 10. (a) / Fdx (b) dx (c)

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Q: A management consulting firm has four types of professionals on its staff: Managing consultants, sen...

A: We can calculate the average of hour rate and number of hours by the formula: Mean/Average = X1*F1 +...

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A: We can use Lamis theorem to find the tension in the cables. 

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Q: 17. /x(2- x)° dx 1/3

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Q: xy cos.x f(x, y) =+3y²

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Q: A car dealer buys 5 cars. Their purchase prices are recorded in a vector: PP = In addition to the p...

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Q: 2. Prove that if m and n are integers and mn is even, then m is even or n is even.

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Q: Directions: Solve the following by getting their derivatives. 4x3-2 1. f(x) x2-5x+1 2. (InVx) 3. у %...

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Q: Lindg @ X= L

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want...

Q: S csch-x coth x dx

A: Given,             ∫csch2x cothx dx

Q: ) Assume (XA) is a Eagebra ond ld ycx be an anbitrary subset. Show that the Family of sets Bi=}unylu...

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Q: Assume the domain of each of the vector fields pictured is R. Which, if any, of the vector fields ar...

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Q: III. Find the bearing. 4.) The vertical ray points to due north. 240

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Q: Consider a set of integers from 1 - 10. G = {1,2,3,4,5,6,7,8,9,10} Answer the following questions: ...

A: (i). Given G = {1,2,3,4,5,6,7,8,9,10}

Q: None

A: Given,             R=(1; 2); (1; 6); (2; 4); (3; 4); (3; 8)S=(2; u); (4; s); (4; t); (6; t); (8; u)

Q: y' + y = 8 (t – 3), y(0) = 1, y (0) = 0 Find y (). ( sqrt(2) means v2) sqrt(2)/2 -sqrt(2)/2 1 -1 sqr...

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Q: nsider the differential equation z' = (e" – 1)(x - 3)(5- a) • a) Find the equilibrium points. b) Gra...

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Q: 1 2. Р. 2 2 D 3

A: Power of a matrix using PDP^-1

Q: Disprove the following statements using counterexample. Explain your answers. 4. x >x 5. x Sx?

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Q: Find the solution of the following second order differential equation d²y(x) dy + x +x2 y(x) = 0 dx2...

A: Given: The second order differential equation, x2d2ydx2+xdydx+x2y=0, where y=yx   To determine: The ...

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Q: Question 2 Let joint pdf for X and Y as follow: f (x, y) = *(2-y) 4 for 0<x<2 and 0<y<2 a) b) Find t...

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Q: Exercice 3 : Solve the first order PDE: Uz + 2u, + (2r - y)u = (2a +3xy-2y)(x+2y) %3D

A: