2. Prove that a positive integer n is even if and only if nis even.

Q: A² = x²y 2 + 2y = y + 3 z ³² x ² 2 5 근 SD • A dv = ? (Do > y 2 - 2 d 1 divergence)

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: max Z= 3x₁ + 2x₂ -X1 + X₂ ≤4 3x₁ + 2x₂ ≤ 125 X1 X₂ ≤3 X1, X₂ ≥ 0

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Q: If A = i - 2j-2k, B = 6i +3j + 2k, find A.B if 0 = 70 7.182 4.897 12.5 O 5.12

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Q: in in words how is derivative lated2

A: We have to explain in the words how derivative is calculated.

Q: Ex.3 The numerical series (n+1)! n=0 5-n! (A) has the same behavior of (n+1)! n=0 (B) is…

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Q: The general solution of the system of coupled equations2r+ay, be + cy can be written as [6] [³₁] +…

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Q: (a) Sketch the graph of the line equation: 2 y = x-1

A: Graph of the line equation

Q: that the function. 22²2² Bin 12 f(x) == x2 0 (x=0) of bounded variation on [1,1]. کر ۔ (x+0)

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Q: task 2a) solve the integral S. S dydx r(1+y²) by switching the integration order, characters are…

A: Given integral  ∫02∫0x 1x1+y2dydx Hence the limits  are  y=x ,y=0 x=0,x=2 So the region is bounded…

Q: b) let R be the disk in the xx-plane centered at the point (0.2) and with radius 2. Calculate ☞² +…

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Q: 13. Consider the function f, such that f and f' are continuous for t≥ 0, defined by f(t)= (871-197…

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Q: 2. Given that f(t) = f cos x cos(t − x) dx, fin integral.

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Q: 8)The dependent variable in a relation is usually placed in the and on the axis in a graph. a)…

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

Q: Find a differential equation that corresponds to the given Hirection field. Consider differential…

A: Here we consider all possible cases.

Q: In the process of calculating the inverse LaPlace of the function. F(s) = -22- arctan (15) you…

A: Given, F(s) = -22·tan-116s

Q: []-[462] [] 16 || x(0) = 4, y(0) = 4 +

A: Given that: x'y'=42-16-4xy,x0=4,y0=4 The objective is to solve the given matrix. Let consider,…

Q: The result of A-(B x C)+ Ax (B.C) may be: 10 21+3j O E 21+2j-k

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Q: The system of equations []=[ -1 -2 -5 ³3] [#] is is to be solved using the forward Euler method with…

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Q: 47. The tower and the cliff has a total height of (85 +110) or 195 feet. If the angle of depression…

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Q: Solve the given differential equation. All solutions should be found. dy =e7x + 1ly dx NOTE: Use c…

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Q: A hole of radius 3 is bored through the center of a sphere of radius 5. Let the cross-section of the…

A: Sol.

Q: 1.047 4Q. Using De Movier's Theorem find all roots of √√25 el

A: The given problem is to find the roots of the given complex expression using De Movier's theroem.

Q: 3. Considere la función e-2 sit > 5 f(t) = 2t si 0≤ t ≤ 5 To calculate {f(t)} using the definition,…

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Q: The roots of the complex number z = (2)¹/2 is Wo = √2 [cos+ i sin], w₁ = √2 [cos+ i sin true false

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Q: 2. Given matrix A = find sin(At). -8 -5 has eigenvalues of 2, 2₂-3.Using Caley-Hamilton theorem, 5 2…

A: Consider the given matrix, A=-8-552 since, it is given that the eigen values of λ1,λ2=-3 so, it…

Q: Let F: R² R2 be the conservative vector field defined by F(x, y) = (exy. -ey) and lety: RR be a…

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Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

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Q: The area between y = x² and y - x³ - 4x from x = 0 to x = 2 is 4.05 3 2.08 5.4 O

A: We can compute the area between the curves using the double integration method. We have to consider…

Q: 3x²y dx − (x³ + y³)dy = 0, y(1) = −2

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Q: Q4: Using Newton Raphson Method determine the root of sin(x) - x/5= 0, answer the following assuming…

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Q: 4. Solve the following using logarithms. a) log x + log(x - 1) = log 2 b) log 40 - log10 = logx

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Q: The boundary value problem y" + y + y = x, y' (1) = 1, y(2) = 2 is solved using central differences…

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Q: Let S = { 1 - (-¹)" | n € N}. Determine inf S and sup S. Justify. n

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Q: 2. Evaluate each of the following. Show all steps/work. b) y = log6 216 a) y = log, 243

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Q: [1-3] 0 3. Find all values of for which the matrix 0 -5 +2 0 3 0 2+5] is singular.

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Q: Find the quotient and remainder on dividing 6x² + 8x +3 by 3x + 1. The quotient is

A: Like two numbers, division can be performed between two polynomials also. In division of two…

Q: 2. Given vectors and with || = 8 and || = 13 and an angle of 50° between them. a) Find |ỹ - ū

A: Let us solve the given vector problem in the next step.

Q: The differential equation 20x+x²y=2x+3₁ (0)=5 is dx O linear with fixed constants O undeterminable…

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Q: Which of the following is a tautology? a. (pvq) →q b. (p^q) →q c. (pv ~q) →q d. (p^~q) →q a Ob O C…

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Q: 1. [A-10] Emma is on a 50 m high bridge and sees two boats anchored below. From her position, boat A…

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Q: Task 5 (Show manual calculations for this exercise) Let the partial differential equation J²u U= J²u…

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Q: Find the Fourier transform of of 6e-ltl.

A: We find the F.T.(Fourier transform) of 6e-|t|.

Q: f(x,y) = (x + y ³) - Sin (x4) (0,0) { 1/₁2 X- 1 (x₁4) = (0,0) is given which of the following…

A: The given problem is to check the existence of the partial derivatives of the given function at…

Q: Let the universe of discourse be the set of all real numbers R. Use the quantifiers and logical…

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Q: 16 Solve the equation using Jacobi's method until 5 iterations. (Non-anonymous question (1) 5x₁ - x₂…

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Q: dy ² dx d²y dx² ey

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Q: Consider the following propositions associated with the study of the +∞ dx J - 1.1² √6 +1 improper…

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Q: Solve the given initial value problem. O x³y²y³ = -18 Oxy² - xy³ = 36 Oxy² + x³ = -18 O x³y² + x³ =…

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Q: 5. Given a piecewise function 4, f(t): = { 1, 0≤t 2. Express f(t) in the form of unit step function.…

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Q: 1. Let X be a topological space and be an equivalence relation on the elements of X. Define : X→ X/~…

A: Please check the answer in next step