Calculate the approximate to the integral -5 (24 +2x² − 3)dx, by the composite midpoint rule with the increment h₁ = 2, h₂: 1. • by the composite Simpson rule with the increment h₁ = 4, h₂ = 2.

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A: It is given that fx=x3+9x2-21x+20. The first derivative of fx is f'x=3x2+18x-21 and the second…

Q: Question # 55: Consider the following data set: X f(x) -0.1 -0.09483 0 0 for a function f (x) For…

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Q: 2. Using the Laplace transform find the solution for the following equatic a y(t) = e(-31) With the…

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Q: The differential equation ax - x-2y+3 2x+3y-4 is reduced to [homogenous or separable

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Q: Do as indicated. 1. Determine the maximum point of the the graph of y = 1- 2 sin(2x), for x = [-,…

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Q: Nathan would like to buy a new car worth PhP 1,200,000.00. He decided to take an from a car…

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Q: For all x € R, it is known that 1. Find the value of f(2022) (0). f()=xe +∞ 3" (n + 1) n! 2. Find…

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Q: O Evaluate the path integral between the points A = (1,3) and B = (2,5) of: (x²y + 2y)dy, with y =…

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Q: 3t 1+f3.y te Consider the parametric equations x = 3t² ‡ 1+ 3,¹ -1. Its graph looks like this: = (a)…

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Q: 2. (x²+6x+5)3/2 dx

A: As per the guidelines I am answering only one question. You have asked to answer 2 and 3 but I am…

Q: Which of the following is a saddle point of th f (x, y) = x³ + y³ + 3y² − 3x − 9y + 2 ○ (1,3)…

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Q: If C is any closed contour around the point z=−1 calculate the value of the imaginary part of the…

A: Here we can use Cauchy Integral Formula to solve this problem. Cauchy Integral Formula Suppose f(z)…

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Q: Let H≤G & KG. Show that HnKH. Let H◄ G & K G and assume that Hn K = {e}. Show that if aeH & beK then…

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Q: Consider matrix attatched and vectors attatched, Let w = Ax+y. Write down w2.

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Q: 1. Evaluate the following integral 1 = [² x(x + 1) 6 (2³ − x) dx -

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Q: (i) A pixie can climb stairs one, two or four steps at a time. Find a recurrence relation for an:…

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Q: x1 + x2 + x3 2x1 + 3x2 + 4x3 3x1 +4x2+2x3 6 20 = 17. = =

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Q: B/ Express f(x) = cos wx, - < x < π, as a Fourier series. Hence prove that 2w 2w 2w + + π(ω2 – 12)…

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Q: Seive the initial valuo problem x'(t)=Axt) for ta 0, with x(0)-(2,1) Classify the nature of the…

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Q: If f and g are polynomial functions in one variable, then ſª¹₂ fő³ 8¹(v) tan−¹(g(x))dydx = (fº°…

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Q: Find the edge chromatic number of Kₙ when n is a positive integer.

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Q: Define f (x,y) = 3y √1+x² a. Find the rate of change of f at the point (-1, 1) along the direction .…

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Q: (a) (i) (ii) In the diagram below, M, L and K are points on the surface of the earth. (n-3.142 and…

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Q: For the system of two equations: 2x + y = 1 -2x - y = 0 Find a solution using the projective plane…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 3. Let H≤ G. Then the number of left cosets of H in G is [G:H]. *True *False

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Q: Consider the initial value problem: ty" - 2t2y" + 3ty' - 3y = t², y(1) = 1, y' (1) = 0, y" (1) = 1…

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Q: Find the streamlines of the flows associated with the complex function Z SOLUTION The streamlines…

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Q: 5. Use the Lagrange multiplier method to find stationary point(s) for the following function.…

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Q: (a) Find the critical numbers of the function f(x) = x(x - 2)5. X= (smallest value) x= (largest…

A: a) Find the critical numbers of the function fx=x6x-25.   b) Tell about the behavior of f at these…

Q: Consider the following system of equations. 2x1 + X2 + *3 = b1 X₁ - 3x₂ + 4x3 = ₂ -X1 + x3 = 3 (a)…

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Q: 1. Derive the Secant formula using geometrical illustrations. 2. Hence approximate the root of the…

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Q: If C is the unit circle x² + y² = 1 oriented counterclockwise and F(x, y) = x F. dR? -T 2π TT î 1 C…

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Q: 6. Maximizing the below profit function with respect to the constraint, evaluate if a solution…

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Q: In the following problems, find the mean value of the given function over the specified region R.…

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Q: without using any kind of label, comment one of Sylow's theorems and define Galois group of an…

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Q: 3. Use Stokes' theorem to evaluate the integral F. dr where C is the curve given by the intersection…

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Q: function. Write f(x) = cos(asin-'(x)}) as a polynomial function, then graph the

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Q: For any two rationals a//b and c//d where a, b, c, d not equal to 0 ∈ Z, the product is given by…

A: The given statement is " For any two rational a//b and c//d where a, b, c, d not equal to 0 ∈ Z, the…

Q: (a) Determine Aut(Z2 © Z₂).

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Q: et H be a HIlbert space and S b of S is a closed linear space of

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Q: Let F be a field and a(x), b(x) = F[x] not both zero. The greatest common divisor (gcd) of a(x) and…

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Q: Suppose is the surface generated by revolving the curve y = 4(x² - 1) about the y-axis. 1. Determine…

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Q: For all x € R, it is known that 1. Find the value of ƒ(2022) (0). +∞ 2. Find the exact value of +∞…

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Q: A smooth curve C is defined by some vector function R(t) with R (-) = (7,0,−2) and R′(t) = (2, √5…

A: Introduction: The moving trihedral of a vector curve is its unit tangent vector, unit normal vector…

Q: For the following systems of equations System 1 x-y=5 2x + y = 1 System 2 x=y=5 -2x + 2y = -10 6…

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Q: QUESTION 1 Given that = 0.2836 approximates f(x) = cos x at x = 5. 1. Find the absolute error 2.…

A: Solution: True value of f(x) = cos x at x = 5 (radian) is         f(5) = cos(5) = 0.2836621855. So…

Q: Show that a lattice is distributed if and only if for any elements a, b, c in the lattice (avb)^с ≤…

A: To Show- Show that a lattice is distributed if and only if for any elements a, b, c in the lattice a…