A scientist uses the one-point Gauss quadrature rule based on getting exact results of integration for functions f(x) = 1 and x. The one-point Gauss quadrature rule approximation for f(x) dx is a

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A: Set: A well-defined collection of objects or elements is called a set. We can represent a set in…

Q: 10) If f(z) is analytic at all points in the region bounded by the simple closed curves C₁ and C₂…

A: Let f(z) is analytic at all points in the region bounded by the simple closed curves C1 and C2

Q: 1. Write the equation of the line containing the points (-3, 4) and (2,5) in the form Ax+By = C. 2.…

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Q: 3. Find the maximum and minimum values of z-a 1-āz on 21 (where a with a < 1 is fixed)

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Q: Q3. Test the following series for being convergent or divergent: (2) Σ (3η)! n!(n+1)!(n+2)! (c) Σ…

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Q: Arithmetic between 30 and 75

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Q: • Create a symmetric equation of a line with the digits 6, 8 and 4. Does the point D (7,-1,8) lie on…

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Q: ( Minimize z = (x₁ − 4)² + (x₂-4)² subject to 2x₁ + 3x₂ ≥ 6 -3x1-2x2 ≥-12 x₂20;x₂20

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Q: Explain how the cosine and sine functions are defined. Think about the unit circle and right…

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Q: Find solutions which satisfy initial conditions: 13. y"+y = 0, y(0) = 1, y'(0) = 0; 14. y"" y = 0, y…

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Q: 3. Find the maximum and minimum values of |-| on |z| ≤ 1 (where a with lal < 1 is fixed) 1

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Q: M rs u and v are given by: u=5i-4j+pk v=2i+tj-3k (a) Express p in terms of when u and v are…

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A: The logistic growth rate model always produces an exponential function. If the model contains the…

Q: . The given family of functions is the general solution of the differential ec licated interval.…

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Q: 7.) Solve а) y'+y'-by=0 6-) у"-ну' +13y=0 с.) у" -бу' +ац=0

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Q: is R* is contractible?

A: This is a problem of Topology.

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A: We have to find the values of x for which the gradient of the tangent to the graph of y=f(x) is…

Q: Let S be the solid of integration of the given integral Q. (1.) Sketch S and label its boundaries.…

A: Q=∫02∫-4-y20∫x2+y28-x2-y2ydzdxdyRegion of integration,0≤y≤2-4-y2≤x≤0and x2+y2≤z≤8-x2-y2

Q: ? For the sequence 2, 8, 32, ...; Write the formula for the general term and use it to find ts

A: To find the general term and 8th term  of the given sequence :-

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Q: Evaluate the Cauchy principal value of 2 x 50% -dx 8 x 2 (x² + 1)²

A: We have to find Cauchy Principal Value of the given integral.

Q: (b) Determine all ordered pairs (a, b) so that the linear system below has infinitely many…

A: Given linear system is ,                    x+y+az = 1x+ay+z = 4x+y+az= b (.)  Consider the linear…

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Q: A subset (a,b) ≤R is T2-space in (R,Tu) * 1 true 2 False

A: Given: A subset (a, b)⊆ℝ is T2-space in ℝ, Tu. To determine: Whether given statement is true or…

Q: = Given the first-difference equation Ayt = 2 and assuming yo method: e, then using the iterative

A: This is a problem of the difference equation.

Q: Let X and Y be two topological spaces. X is connected and Y is disconnected are they homotopy…

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Q: Write the general solution if the ODE and its solutions are given as follows. y (4) + y" = 0 ;…

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Q: solve by finite difference ²x - ²)x=t dt²

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Q: Find the vectors u and v whose initial and terminal points are given. Initial Point Terminal Point…

A: Find the vectors u and v whose initial and terminal points are given.        Initial Point  Terminal…

Q: In Problems 17-20, expand f(z) = annular domain 0 <z - 2 <3 N (z + 1)(z-2) in a Laurent series valid…

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Q: LEARNING TASK A Directions: Write Yes, if the two triangles are congruent and No if not. State the…

A: State the congruency of the figure 1.

Q: Let S be the solid of integration of the given integral Q. (1.) Sketch S and label its boundaries.…

A: From limit of given integral we will find the region bounded and then draw the diagram . While…

Q: The given functions are concave or convex or neither in the domain: 1). f(x, y) = 2r-y-r²+2ry-y² 2).…

A: As per the question we are given two multivariate quadratic equations : f(x,y) = 2x - y - x2 + 2xy…

Q: Consider the surface S given by: S: r(u, v) = (uv, u, u²+v³), u € [0, 1], v € [0,2] whose graphic…

A: Given- Consider the surface S given by: S : ru, v = uv, u, u2 + v2, u ∈ 0, 1, v ∈ 0, 2 whose graphic…

Q: 8*. For each of the following functions, determine which, if any, of the following conditions the…

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Q: 3x+4y-2z+ cos6x+9 exp(x)=-9 5x+2y+z=-3 x-y+5z=-11

A: Note:- This system contains some trigonometric terms. so, we'll use graphical method for solution.…

Q: (i) Sketch the graph of y = cos x for 0° ≤ x ≤ 360°. On the same axes, sketch the graph of y = cos…

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Q: x+4v-2z+

A: find the value of x,y,z using three equations

Q: 3. Find the maximum and minimum values of z-a 1-āz on 2 ≤ 1 (where a with la| < 1 is fixed)

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Q: 1 A=-1 -1 1 1 1 det A =

A: The following steps are used to obtain the solution. Enter the matrix A at the MATLAB prompt ≫. Use…

Q: 1. Let 1, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1…

A: \documentclass{article}\usepackage{amsmath,amssymb}\begin{document} (a) Norm x=Norm y=1\\ Let angle…

Q: 3) When expenses are taken into account, the linear model will shift. For example, prior to working…

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Q: (B) Find the zero-divisors of Z6.

A: Here we have to find zero divisors of Z6 .

Q: 1 8) Find the Laurent series of f(z) = (2-1)(z-2) ****** **** b) ·+ + + + + 3² +22² +2³ + 18 c) I d)…

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Q: 2°) Write the volume integral of the solid bounded by 2 = √ x² + y²² and 2= √√2-x²-y²¹, in a)…

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Q: Use the limit comparison test to determine whether the series E=1 * (k+1)(k+2)(k+5) converges. A…

A: The given series: ∑k=1∞kkk+3k+1k+2k+5 Limit comparison test:  Consider two series ∑nan and ∑nbn. If…

Q: 3.2. The least squares solution of smallest norm of th in m x n matrix, is given by

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Q: 2. Let A € M, (R) be given. (a) If AA = 0n, prove that A = 0₁. Does this hold if A € M₂, (C)? (b)…

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Q: 2. x=9-y², y-axis; about x = 9

A: Given that region is bounded byx=9-y2⇒x =(3-y)(3+y) and y-axis ; revolving about x =9