Use the three-point Gauss-Legendre formula to evaluate the integral dx Ső (2x + 1)²

Q: K(G) < K'(G) < 8(G).

A: For a graph G ; κ(G)=Vertex connectivityκ'(G)= Edge coonectivityδ(G)=Minimum degree of G

Q: 7.Find xy of z = 2x³-5xy²

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A: Given: Let us consider the given, r=1+12+13+...+1p-1

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Q: dªy Using the reduction of order method, find the general solution of the differential equation dx4…

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Q: Show that the equation 2²2 2 2²y Əy +2k c². əx² de ² Ət possesses solutions of the form 0 - kt Σ Cre…

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Q: Commencing with the Cobb-Douglas function below: q(K, L) = K¹/4L3/4 Optimize q subject to the…

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Q: f(x, y) = x² − 4x³ + 2y² + 8xy+1 -

A: According to the guidelines I am answering first question only.

Q: Consider the following optimisation problem min f(x, y) = x + y − x2 subject to x + y ≤ 1 x ≥ 0, y ≥…

A: As per the question we are given a optimization problem as : min(x,y) x+y-x2 s.t. x+y≤1 ; x≥0 ; y≥0…

Q: determine the value of s, v, and a using determinant method: s+2v+2a=4 3s-v+4a=25 3s+2v-a=-4

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Q: C -9 -3-15 0 -7 0 -6 5. Let A = where c is an unknown scalar. " 0 7 2 13 0 40 3 (a) Without using…

A: Given :                      A = c-9-3-150-7   0-60   7   2  130   0   03  Now for characteristic…

Q: 2 2. y² dx + ( x² + 3xy + 4 y²) dy = 0 when x = 2, y = 1

A: Solution :-

Q: 5. Lim xsinx x+0+

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Q: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

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Q: Compute for a real root of 2 cos sin √ = accurate to 4 significant figures using Fixed-Point…

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Q: use Newton’s Method to find all the roots of the given equation accurate to six decimal places.

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Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: f( x) = sinx - x3 + 1 By Midpoint method f'(a) = (f(a+h) - f(a-h)) /2h

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Q: Starting with the given fact that the type 1 improper integral dx converges to p-1 1 when p>1, use…

A: Value of type-II improper integral

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Q: Let ƒ be a mapping from [2, +∞ [to, +∞[defined by: 3 f(x) = x + = x f has a fixed point. O False O…

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Q: 3x y"+y= e¯x2 - 4x + 2x² + e³x 8-12x - 10x²

A: Let us consider the given differential equation y''+ay'+by=Q(x) To solve the differential equation…

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Q: Let

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Q: Suppose the rule ²[ƒ(-2,−1)+4ƒ(−2,0) + ƒ(−2,1)+ ƒ (2,−1)+4ƒ (2,0)+ƒ(2,1)] applied to 12 solve f(x,y)…

A: Given: The rule, 23f-2,-1+4f-2,0+f-2,1+f2,-1+4f2,0+f2,1 is applied to solve ∫-11∫-22fx,ydxdy.   To…

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A: Solutions

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Q: 9. (a) Use the method of Lagrange multipliers to determine the minimum and maximu values of f(x, y)…

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Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 2x³+2x²+2x+6 1. Lim X→2…

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Q: Prove that if f, g area analytic at ro and g(ro) #0 then f/g is analytic at ro

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Q: The equation of a hyperbola given below when reduced to standard form is 16y² −9x² +36x + 96y - 36 =…

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Q: Based on the image attached, solve the following questions. i) Express graph the system by using a…

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Q: theormo- Let (Ft) is a field and f(x) EF(x) then the ideal ismaximals ideal iff fex) is an…

A: Let , F , + , ·  be Field. Given that  , fx ∈ Fx. Let , f(x) is maximal ideal. We need to show that…

Q: Determine inverse z-transform of the following equations: 2² b. (2-1)(z-0.5)

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Q: la² + 2a 2a + 1 1 2a +1 a+2 1 31 3= (a- 1)³ 1

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Q: Suppose T: R¹4 → R¹4 is a linear transformation and the rank of T is 10. 2. (a) Determine whether T…

A: The solution is given as

Q: a) Prove that an operator P is the pr osed linear subspace M of a Hilbert

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A: Draw and label the diagram depicting this scenario. Use law of cosines to determine the distance.

Q: c) Using the Euler-Lagrange equation of the Calculus of Variations Optimize (-16y² + 144y + 11yy' −…

A: Given functional is ,                                            I[y(x)]=…

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Q: Calculate the points of intersection of the curves x² = 4y and bn=) = y 29vaus at newed biloa gris 1…

A: Centroid: The centroid or centre of mass of a region bounded by the curves is the point where the…

Q: Using the Euler-Lagrange equation of the Calculus of Variations Optimize (-16y² + 144y + 11yy' -…

A: