a) Find the area of R. (b) SET UP a (sum of) definite integral(s) that is equal to the arc length of the portion of the curve y = √x -3 which serves as a boundary of R. (c) Use the WASHER METHOD to set up (a sum of) definite integral(s) that is equal to the volume generated when R is revolved about the line x = 9.

Q: 4. When solving for the solution of higher order differential equations, the presence of x in the…

A: NOTE:Kindly repost the other question as a separate question.  When solving for the solution of…

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Q: NEED ASAP!! By using laplace transform to solve y’-y=cosht with y(0)=0, what would be the particular…

A: First we will take the Laplace transform of both sides then we will use the initial condition y(0) =…

Q: 1. Let G be an abelian group with the identity element e. If H = {x²|x € G} and K = {x € G|x² = e},…

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Q: Evaluate. [ 10.xªtan (2x³ + 3) dx

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Q: Find the roots of the equation using Bisection Method and False position Method. f(x) = e-2x -4 if…

A: We can solve this using Bisection Method and False position Method.

Q: 8.M.2 One can define a bilinear form on R2 by the formula ‹ [ 8 ], [ 8 ]› = ac − 3ad − 3bc + 7bd. a)…

A: We have to find the Gram matrix G of the given bilinear form. Then, we can proceed further.

Q: The volume of the solid bounded by z = 0, x+y+z= 4 and x² + y² = 4 in cylindrical coordinates is 16.…

A: Solution:  True

Q: Find the solution of the following differential equation: d'a dr dz(0) +9x=32, 2(0) = 4, dt² dt…

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Q: N 2 (2-1) (2-0.5)

A: The detailed step is given below. We do the partial fraction by first subtracting adding "1" in the…

Q: 1. Use Newton-Raphson method to find sixth iteration of a real root of the equation: cosx-xe* =0…

A: Formula Used: xn+1 = xn - { f(xn) / f'(xn) } .

Q: Find a power series solution of y" + (1+x²)y = 0 13 a. ao(1-x². x6+)+a₁(x-x³1x5. 24 720 24 13 b.…

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Q: Determine the general parametric solution of the following Lagrange and Clairaut differential…

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

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Q: Q2/ Find the first moment about y-axis of the region in the first quadrant bounded by the x-axis,…

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Q: Evaluate. 3 Lox f(x) dx, f(x) = (−x + 1, x≤2 1-x² + 6x-9, x>2

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Q: What is the area of one petal of the curve r = sin 30 ? AA= sq. units A-3 sq. units B. C. A = π sq.…

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Q: Find the 103rd derivative of cos(2x).   Hint: find the first few derivatives and observe a…

A: First find nth derivative then put n=103 to find the 103rd derivative as in next step.

Q: The orthogonal trajectories of the family of curves y = cx² is (A) 2x +y2=k (B) x²+2y² = k © x=ky² D…

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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: 2. Consider the surface f(x, y) = x² + y² = x² + 2xy - y² - a) Find all critical points of f (Hint,…

A: As we know a saddle point or minimax point is a point on the surface of the graph of a function…

Q: [2 + m 3 1. Given A= 1 a. (AB)¹ - A b. |4A-¹ + 2B-¹| a. 2AB-¹ 1 2 -1 -1 4 5+ ml and B = [-1-m 2 91 3…

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Q: B/Find the oblique asymptote of the function f(x) = -3x²+2 x-1

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Q: Message: [-859] [1943] [1060] [O_25] [-7 81] matrix used: 3] -1 3

A: Given: A=12-13 To use matrix A to decipher the message: [-8  59] [19  43]  [10  60]  [0  25]  [-7…

Q: HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. (D2 – 4D + 4)y = 0 ; when x = 0, y = 1, Dy = – 1.

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Q: 7. Prove that if v >-1/2 ; p) = L{xvJ, (; = xı-at-a) H

A:

Q: y Classify the DE: X- +xy= dy dx X (A) Linear but not Separable (B) Separable but not Linear…

A: Solution

Q: . Find the centroid of the solid generated by the area bounded by y = sin x and the lines x = 0; x =…

A: Since  the area is rotated about x axis ,the y and z coordinates of centroid are 0, and the centroid…

Q: Diagonalize A = 12 0 2 1 0 00 - 3 and compute A2019

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Q: A metal sphere cools from 80°C to 70°C in 5 minutes. How much more time (in minutes) will it take to…

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Q: 1. Two cars start from the same place and travel in opposite directions, one at the rate of 45km/h,…

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Q: Use the method of reduction of order to find a second solution of the differential equation ty" +…

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Q: 6. We always prove an argument. 7. If an argument is true then it is valid. 8. Suppose a declarative…

A: Since you have posted a multi subparts question according to guildlines I will solve first…

Q: 3. Consider the double-integral 2xy² + 2 dx dy where D is the triangle with vertices (0,0), (5, 1)…

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Q: 3. Find a Taylor series for the function f(x) = ln(x) about x = 0.

A: To find: Taylor's series expansion of lnx about x=0.

Q: Find the determinant of the following matrix- (1 x₁ x² ... x7-¹\ 1 2 x2x² x²2 ... 1 In x² : ⠀ ⠀

A:

Q: 4. The statement "p: r is a real number such that r² ≥ 0." is a proposition. 5. If a bird can fly,…

A: A proposition is a statement that can be either true or false; it must be one or the other, and it…

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x) =…

A:

Q: 3. Using the Gauss-Seidel method make three iterations for the linear system x(0) = 0, 4x - y -z =…

A: Solution :-

Q: 2. (Calculus) Evaluate the integral S 1²+2x+3 (x-6)(x²+4) dx

A: For a function g(x) and its derivative is f(x), then; ddx(g(x))=f(x) then; ∫f(x)dx=g(x)+C where C is…

Q: Prove this: A=B iff A° U B = Ω =

A: Solution : First prove left to right, If A⊂B is true , All elements of A are inside B, Then Ac is…

Q: Solve the following differential equations using this method - In both M(x,y)=0 and N(x,y)=0 replace…

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Q: Find the Fourier expansion of th function and dr periods of the

A: Given function: f(x)=x+πif -π<x≤0πif  0<x≤π   To find: Fourier series expansion of given graph…

Q: 【D³ + 3D² + 3D + 2)y = 0

A: Solution:

Q: In Exercises 1 through 8, find all conjugates in C of the given number over the given field. 1. √2…

A: Solution : Conjugate of a real number is, a number which multiply to , The number and it give…

Q: z² 2 (z-1)(z-0.5)

A: Given z - transform ,                                            F[z] = z2(z-1)(z-0.5) Inverse  z -…

Q: Let -3 M=[#4] -4 -3 Find formulas for the entries of M", where n is a positive integer. (Your…

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Q: 10 Estimate ¹0 f(x) dx from the following table, using Simpson's Rule. X 0 1 2 3 4 5 6 7 8 9 f(x) 40…

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Q: Solve the exact differential equation (In y - y sin x-6e³x) dx + ( + cos x + 5 sec y tan y - 6y)dy =…

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Q: 1 Find the Hankel transform of xve-ax, taking xJ, (px) as the kernel.

A: