Q3/ Find the volume of the solid generated by revolving the region bounded by y = 3/(2√x), y = 0 & 1≤x≤4₁ about y-axis

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Q: r3 Consider the integral e dady. (i) Sketch the region of integration. (ii) Change the order of…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

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Q: Let A, B and C be sets. Use an element argument to prove the following. (A - B) n (B-A) = 0.

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Q: Define g(-5) in a way that extends g(x)= 9(-5) = x² - 25 x + 8x + 15 to be continuous at x = -5.

A: We have to define g(-5) such that g(x) is continuous at x = -5.

Q: Evaluate L{3e−2(1−t)+t3e2t+2t2sinh(2t)−4e−2tcos(π−3t)}

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Q: 5. Calculate the L and U matrix and proof that PA=LU. 10 -7 0 A = -3 26 5 -15

A: Firstly I find lower triangular matrix LL and an upper triangular matrix UU And the show that PA=…

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Q: Consider the function f(x) = x = [0,2]. Construct the , Lagrange interpolation polynomial which…

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Q: Six second-order equations and four y(t)-graphs are given below. For each y(t)-graph, determine the…

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Q: ample 8.9. Find the maximum and minimum value of y from the following data -2 1 2 3 4 2 -0.25 0…

A: We need to find maximum and minimum value of y from given table.

Q: Example 8.23. Evaluate using Gauss formula for n = 2 dx 1-1 1+x² and n = 3.

A: The problem is solved using Gauss formulas for n=2 and n=3.

Q: Solve the following simultaneous DE using Laplace transforms. 2 dy fut dx 5 sin t = 0 dt −y+x+ dt dy…

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Q: (d) A commutative ring R is a prime ideal of itself. (e) If p and q are primes, then there is a…

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Q: By using Newton Raphson Method, the repeated root of 4x^3-8x^2-3x+9=0 using 2 as Xn is? O 1.6 1.55…

A: Given equation is 4x3 -8x2 -3x+9=0 Take fx = 4x3 -8x2 -3x+9 First derivative of f(x) is fx = 4x3…

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Q: Solve the following using the inverse matrix method: (Show your solution) 3x + 2y x + 4y b) = 26

A: The solution to the system of equations of the form: AX=B is calculated using the equation: X=A-1B.…

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A: B2C e-commerce means selling the products and services from business to end consumers (B2C) on the…

Q: Six second-order equations and four y(t)-graphs are given below. For each y(t)-graph, determine the…

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Q: Find the feasibility region bounded by the following systems linear inequalities. Find the critical…

A: Draw the lines x+2y=6, 2x-3y=12, x+2y=10, x-y=1, x=0 and y=0 on the graph paper.

Q: Question 3. F Prove each of the following. (a) Given a real number a > 1 with a N, show that there…

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Q: for a quilt using polygon EQFRGSHP shown.

A: Given as,

Q: Given: y' - 2 = −e¯4x – 2y, y(1) = 0.25, h = 0.05. At what value of x will the % error in the…

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Q: Q3:what is the difference between the finite element and finite volume method

A: We have to write the difference between finite element method and finite volume method.

Q: Given the figure below, answer the following questions: B C R E G H 1. The path C to D is consistent…

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Q: 3. fy dy + 10g = e + dt +7 -2t

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Q: Example of a function that is dot convergent but not uniformly convergent

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Q: Solve y" (t) + 2y' (t) + 2y (t) = H (t); y (0) = 1 ; y' (0) = 0 where H(t) = 2t + 3,0 < t < 1 H(t) =…

A: *This problem is too lengthy.That's why I have used partial decomposition calculator to find partial…

Q: Example 8.8. From the table below, for what value of x, y is minimum? Also find this value of y. **…

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

Q: (a) Given a continuous function f RR and a connected subset SER, is f-¹(S) connected? Justify your…

A: Let us define function f : R ---&gt; R by f(x) = x2 Clearly f(x) is continuous  We know that, The…

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Q: JJs where S is the sphere x² + y2 + z2 = 1.

A: Given S is the sphere                         x2+y2+z2=1 To evaluate:             ∫∫S3x+3y+z2dS…

Q: 1 ' Identify the surfaces of the following equations by converting them into equations in the…

A: The Cartesian co-ordinate and cylindrical coordinates are related as…

Q: 2. Find the series solution of the equation xy" + 2y' + xy = 0 in a form: y(x) = y(x)=(ao )=²(ao c…

A: The given problem is to find the series solution for the given differential equation. The given…

Q: Consider the surface S shown on the graph, whose parameterization is given by: r(u, v) = (v², uv,…

A: Given- Consider the surface S shown on the graph, whose parameterization is given by:  ru, v = v2,…

Q: Let 2={1,2,3,4,5,6}. Construct the minimal field containing 1. 8={{1,2}, {3,4}}

A: This is a problem of measure theory.

Q: (B) Give an example for a commutative ring with identity.

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Q: Consider the following families of sets indexed by the set of natural numbers. Which among these is…

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Q: Let f and g be functions which are differentiable on R. For each of the following statements,…

A: (a) The given statement is: "If f'x=g'x for all x, then f0=g0" The statement is false. Take the…

Q: 4. Find the rank of the given matrix below using echelon form. 1 2 4 3 2 5 -6 10 -2 -7 3 21 8 15 12…

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Q: 5. For which value of x do the following vectors form a linearly dependent set in R³ "=(x 글 글(글,…

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Q: постолни тяло beens его вдо колкот - Solue nan-ty ay = nаy - yan и 2 +у2 в (res) 14:09

A: The solution is given as

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Q: By direct partial integration, Solve the following PDES 8- Xd²z 5 4 dz ду = 0, ₂ z(x,0) = x² +X, Z…

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Q: Set-up the iterated double integral in polar coordinates that gives the volume of the solid bounded…

A: The given problem is to set up an double integral in polar coordinates that gives the volume of…

Q: (b) Given two metric spaces X,p>, and a function f : X→ Y that is uniformly continuous on SC X. If…

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Q: Match the formula of the exponential function to its graph. Graphs of Exponential Functions 5 4 3 2…

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Q: Consider a function defined on R² by f(x, y) = y(x + 1)(2 − x − y). (a) Find all four critical…

A: The given problem is to find the critical points of the given function of two variables and also…