Show that the odd numbers and the natural numbers have the same cardinality

Q: 201х, у) — х* — у

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Q: Consider the function f : [0,3] –→ R defined by f (x) = 1 for x E [0, 1), ƒ(x) = 2 for x E [1,2),…

A: We are given a function f:[0,3]→ℝ defined as,   f(x)=1 if 0≤x<12 if 1≤x<23 if 2≤x≤3 We need to…

Q: * = y +z- 4x Solve: dt = x+ 5y - z # = y - 3z

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Q: Converge or diverge?

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Q: x be the Let A is an invertible n xn matrix, and let b be a vector in R". Let x = solution to Ax =…

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Q: A factory has three machines (1, 2, 3) and three jobs/tasks (A, B, C) to be assigned to this…

A: Machine Task A Task B Task C 1 2 12 6 2 7 8 3 3 2 5 6 there are three rows and 3 columns…

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A: Given series is ∑n=1+∞10n2+187n2+16n+21

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Q: the power series E e Limit Comparisor

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Q: Solve for the Laplace transform of sint sin 2t cos t

A: The given function is f(t)=sin t sin2t cost  rewrite the function as  f(t)=122sin t cost sin2t…

Q: 3. Given X'- ( ")* -16 2 -8 sin(2t) (a) Verify that X1(t) = ( cos(2t) + sin(2t) ) * 4 cos(2t) – 4…

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Q: Determine whether the following series converge or diverge. 4+ cos? n •2 3n – Vñ Σ (5 – 4(In n)³)"…

A: Here we can use following test to check the convergence of the given series: (i) Limit comparison…

Q: 1. Consider A = (0, 4, 2) , B =, (6, –1,0) and C = (3,0, 1). (a) Find the unit vector having the…

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Q: Solve the differential equations by the Power Series method: y" + x²y' + xy = 0.(Please write two…

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Q: Consider the function if g(x) = if 2. if x>0. And study its continuity at x=0

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Q: (b) Fourth-order Adam's Method Use previously computed values at ri-3 = -2.306160, yi-1 =-0.3929953,…

A: Given differential equation is dydx=4e0.8x-0.5y with initial condition y(x0)=2, 0≤x≤4 step size h=1…

Q: What are the first four terms of a Maclaurin series for y(x) = (1+ x)-3 ? Show each step of your…

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Q: 2. Solve the following differential equations: (a) y' e2y = (b) y' = 1+ Y (c) xy' = y(3 – x)

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Q: Find two power series solutions of the given differential equation about the ordinary point x = 0:…

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Q: S+o (4-x)" V(n+5) +00 Consider the power series n: 2n=1 9n · 7" D. Find the radius and interval of…

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Q: IV. Determine if the given is convergent or divergent. 1. dx (x2 + 1)² 1

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Q: 1 2n Consider an = %3D tan-1 n 1. Determine if the sequence {an}n=1 converges or diverges. 2. Is the…

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Q: $20,000 is invested for 9 months at an annual simple interest rate of 3%. (a) How much interest…

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Q: 4 - 2v2. R

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Q: A mathematical model for the rate at which a drug disseminates into the bloodstream is given by dx…

A: To use phase portrait we will find equilibrium line and then find limiting value of solution . For…

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Q: Solve for the square root of-i a. b. - C. d. Both a and c e. None of these

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Q: Consider the general form of AT Ax = ATb used to find the line of best fit C+ Dt throu (t1, b1),…

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Q: Which of the following sequences of values (inserted in order, from top to bottom) would correctly…

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Q: (16) s: 5: 2n + 1 n=0

A: In this question, the concept of sequence and series is applied. Sequence and Series A series is…

Q: 8. The water depth in a harbour is m at high tide (fill the with any number between 25 and 35) and m…

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Q: s+2 Let F(s) = and f(t) denote the inverse Laplace transformation of 3 2 4 F(s). Find the exact…

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Q: Find the general solution of the given differential equation. + y = e5x dx y(x) Give the largest…

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Q: 3. Consider the function f(x) = 2x² – x on the interval [1,6). %3D (a) For n = 5, calculate Ax and…

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Q: Determine which (if any) of the following series are conditionally convergent Α. Σ-1" sin (n) C.…

A: I just answered which are convergent

Q: COS“ n In n n2 n3 n=1

A: Given :  The given series is   ∑unn=1∞ = ∑n=1∞cos2nn2 + ln nn3. To prove : We have to determine…

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Q: IV. Determine if the given is convergent or divergent. n Σ #2. L in? + 1)² n=1 %23

A: To find Whether the series converges or diverges.

Q: n all yER Fim a powes cypnesentation for sehjes growes Y?cos (2x) 4 thn by dfferemtiatinn suow unt…

A: We have to show that the sum of given series.

Q: In this exercise, use the region under the graph of f(x) = 6x + 8, above the x-axis, and between the…

A: The given function is f(x)=6x3+8. In the given problem we have to find the region under the graph…

Q: 6. Find the standard matrix of the linear transformation T: R2 → R? that first reflects through the…

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Q: Use the 3rd degree Maclaurin polynomial for g(x) = r cos Write your answer in decimal form. to…

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Q: Consider the following linear map T: P3 → P3 defined as follows: T(ao + a1x+ azx² + a3x³) = ao +…

A: For T to be an isomorphism we must check that it is one one and onto both. And we can check it by…

Q: The power series to (4-x)" /(n+5) Zm=1 9n · 7n 1. Use Alternating Series Test to show that the…

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Q: -2n2n 2n n 2) п En=1 1 —

A: Given series is ∑n=1∞1-2n2nn2n

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Q: bh + 2 T XT A = 2 Find b Find h Find r

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Q: Five Computer Programmers have been told by their company Computer and Information Technology…

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Q: Q7. Construct an undirected network diagram using the given set of nodes and arcs: Nodes (A, B. C.…

A: Given nodes are:{A,B,C,D,E}