Prove by induction Ein (-i)i ;2= (-1)" n(n+1) i=o 2

Q: The wave equation = may be studied by separation of variables: u(x, t) = X(x)T(t). If(x) = -k² X(x),…

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Q: (b) Prove that 2m ≤ m! + 2 for m ¤ N. (c) For any nonzero real number x, prove ---3 i=1 = 1- x -n

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Q: Solve the following

A: Given,           2x-5y=2-4x+10y=1

Q: The set S=[1,3) is not compact. Which open cover of Scontains a finite subcover? ○ { [1, 3 + 1/n) |…

A: Open cover: Let S⊂ℝ and U=Uα : α∈I be a collection of open subsets of ℝ, where I is an indexing set.…

Q: A natural number n is even if n = 2k for some kw. If n = 2 i + 1 for some i Ew, then n is odd. Prove…

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Q: 4. 5. For n E N, { x ER | |x-x*|<1/n } is open. UA_n is open where A_n=(n-1,n).

A: To determine: If the given statements are always true, sometimes true, or never true: (4.) For n∈ℕ,…

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z)= -3ry-lysj-Szak…

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Q: Basic PDEs Which of the following statements is guaranteed to be true? a O [y + 2x² cos(y)] = 1- 2x²…

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Q: The position of a particle moving along a straight line is given by the function S(t) = 2sint +…

A: Direction of particle depends on sign of its velocity

Q: Find the cardinal number of each of the following sets. Assume the pattern continues in each part.…

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Q: Use LU decomposition method to solve the system of equation. (Show your solution) X1 + x2 + x3 = 1…

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Q: Which of the following integrals correctly solve for the magnetic flux passing through the surface…

A: We can solve this using magnetic flux formula

Q: Example Verify y, and y satisfy the corresponding homogeneous D.E. Then find a particular solution…

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Q: */ Find the solution to the following linear programming problem by dual simplex method Min Z=…

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Q: Question 1. 1. Use the operations in o-algebra, such as union, intersection, difference, countable…

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Q: et f(x) = n 0, if xe Qor x = 0 if x= min lowest term . Compute for ff. " n

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Q: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

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Q: Solve the following using Cramer's rule: (Show your solution) 3y (a) 4x + 4y |||| 12

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Q: Draw a direction field for the differential equation y' = -y(10 - y). Based on the direction field,…

A: Option are not given , please check and match.

Q: 3. A curved lamina is in the shape of the surface defined by R(u, v) = (u cos v, u + v, u sin v),…

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Q: The set S=[1,3) is not compact. Which open cover of S contains a finite subcover?

A: This is the question of Topology.

Q: 1. A student listed 10 of his classmates' scores: 34, 42, 27, 34, 45, 32, 31, 44, 33, 31 a.…

A: Mean: Mean is the average of a given data set.             i.e. to find the mean of a given data set…

Q: 2- Perform the following inverse Laplace transform using convolution theorem: 3s +1 C-1 2 Wind I S²…

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Q: f(x, y)=√x² + y², y = 1², x = t

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Q: - xy², which vector is normal to the plane tangent to the surface of this function at (0, 0, 0)? If…

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Q: of- 's(s+1)(s+2)

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Q: -5) as golve: x'= -3x + 3y +z -1 (**) x-sy-32 +7 2'=-3x + 74 +32-7 =) i) Does (**) have a solution…

A: As per norms, we will be solving only one question. If you need an answer to others then kindly…

Q: PART#A Use Stokes' Theorem to find the circulation of F= (zy, y, z) around the boundary of the…

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Q: dy = f(y). dt The following problem involves an equation of the form Sketch the graph of f(y) versus…

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Q: e terminal side on the unit -:-)

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Q: c. If you had extra-physical powers and could make a spring with a negative spring constant (but…

A: Given: The harmonic oscillator equation, md2ydt2+bdydt+ky=0. The spring has a negative spring…

Q: ) Suppose that in a class, there are n many boys and n many girls. Among these 2n many people, we…

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Q: 11. Find the equation of a line parallel to 2x+5y = 1, with the same y-intercept as x-4y = 8. Label…

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Q: √ √ (3-6XY) JA where ID is the Evaluate √√√(3-6x9) JA region shown below y=x2 3. 2 y=-x²

A: Let us consider the double integral ∫ab∫f(x)g(x)F(x,y)dydx To solve the integral  Integrate the…

Q: Find all integers n > 1 such that 1” +2^ +...+(n − 1)” is divisible by n.

A: We have to find the all integers n&gt;1 such that 1n+2n+.........+n−1n is divisible by n. Firstly,…

Q: 1. Find A -4A5 for 1025 A = -2 3 -1 2

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Q: A radioactive substance is decaying exponentially. There were 45 grams of the substance initially.…

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Q: How long will it take for your initial investment of $4,775 to reach $7,500 if the money is invested…

A: We are given Principal Amount P=$4775,   Total amount (Principal+Interest) A=$7500,   Interest Rate…

Q: Find the solution to the following recurrence relation: an = 7an-1 for n ≥ 2 with the initial…

A: The given recurrence relation is: an=7an-1 for n≥2 The initial condition is a1=2.

Q: D = 3 1-2 0 0-4 ** 5 -4 5 3

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Q: Problem: The concentration of salt x in a home-made soap maker is given as a function of time by: dx…

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Q: Draw a direction field for the given differential equation. Based on the direction field, determine…

A: To slove the problem

Q: Let ⁄2 be a bounded interval. For any g € L²(2), define the operator T, by T,(f) = f Then T, is a…

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Q: points in a certain category, enter NONE.) x³y" + 5x²y + 2y = 0 regular singular points X NONE…

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Q: convert the following differential equation into a Perfect equation and then Find its general…

A: Solution :

Q: + f(x) af -12 -4 4 -20 -1 12 20 X

A: Solution: f(x)=40≤x&lt;4-14≤x&lt;848≤x&lt;12 Period = 16 Fourier series:…

Q: Which characteristic/s implies(y) that a set S of real numbers is closed? S has no accumulation…

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Q: Let A and B be sets. Prove that if A = B, then A+ = B+.

A: Given: A and B To find: Solution

Q: Convert the following differential equation into a Perfect equation and then Find its general…

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Q: Calculate L{cosau du du du}.

A: Laplace transform of the function