x-x³. Selling how many units will give positive revenue? ... The revenue from the sale of a product is given by the function R= 625x-x Selling more than and less than units will give positive revenue.

Q: Consider the differential equation 4y" – 4y^ + y = 0; ex/2, xex/2 Verify that the functions ex/2 and…

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Q: S (s² + 100) (s − 8) } Evaluate ¹{.

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Q: A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3262…

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Q: Consider the vectors ā₁ 8. , ā₂ = = (a) Write b as a linear combination of a₁, 72, and a3. (b)…

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Q: Suppose that a sporting contest at Adelaide oval, which has capacity for 50000 spectators, draws an…

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Q: Let T(x): be the taylor polynomial of degree k of the function f(x) = sin(x) at a = 0. Suppose you…

A: Given function is f(x)=sin(x) Since Taylor polynomial of sin(x) about a=0 is f(x)=sin(x)⇒…

Q: GRAD, DIV, CURL, V², DIRECTIONAL DERIVATIVE 36-45 Let f zy + yx, v = = Find 36. grad f and ƒ grad ƒ…

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Q: 34 x 5 i. 61 × 30 17. Practice multiplying without using a calculator. Try using different…

A: Note: Since we can solve at most three subparts in a question, we have solved the third three…

Q: Let D = {0,1,c,d} be an integral domain. Explain why the following are true: (1) If 4.1=0 then 2.1 =…

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Q: Find the first four nonzero terms in a power series expansion of the solution to the given initial…

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Q: Find the derivative of the function. sin(x) y = In(1 + 7v) dv g'(x) = Jcos(x)

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Q: 1. Find the radius of convergence of (-x)³n 8n (2n + 1)* n=0 In addition, analyze its convergence at…

A: Given series is ∑n=0∞-x3n8n(2n+1)

Q: Finding the Volume of a Solid In Exercises 26-28, use the shell method to find the volume of the…

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Q: In Exercises 9-12, show that the Gauss-Seidel method diverges for the given system using the initial…

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Q: hod is used to so +6x8 = 0. Tak e solution obtai

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Q: Find the general solution of the system of equations 8 -4 t x': (₁ 1 ) x + ( ++ ³2₂) ₁ ² > t> 0. 16…

A: Using method of variation of parameters

Q: 3) Let ƒ : (0, ∞) → C denote a bounded continuous function. The Laplace transform of f = f(x) is…

A: Given that gx=12πilimR→∞∫?c,R1zexzdz Then by the Cauchy's integral formula, such that…

Q: HIY x+y+1 1. Let f(x,y) (a) f(2,1) (b) f(1,2) (c) f(a, a) (d) f(y+1,y) Find:

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Q: Residue of

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Q: 17. Consider the DE y"+by'+cy = 0. If y₁ is a solution of the equation, what conditions must be…

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Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

A: Given equation of plane P1: z=4-2x  Equation of paraboloid P2:z=4-x2-y2 We know that volume of the…

Q: 5. Determine whether the following improper integrals are convergent or divergent. (a) sin (x²) x7/2…

A: Thank you for the question. Since you have asked multiple questions, we will solve the first…

Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,c),(b,b),(b,a)(c,a)(c,d) and…

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Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

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Q: Assume that y is the solution of the initial-value problem y' - If y is written as a power series Σ…

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Q: Use the Laplace transform to solve the given system of differential e dx 4x + d³y dt3 = 12 sin(t) dt…

A: dxdt−4x+d3ydt3=12sintdxdt+2x−2d3ydt3=0x0=0, y0=0, y'0=0, y''0=0

Q: 2. Let C be the graph of R(t) = (t sint, t³). a. Using the definition, show that Ŕ(t) is continuous…

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Q: Use the divergence theorem to calculate the surface integral F · dS; that is, calculate the flux of…

A: We have to use divergence theorem to calculate the surface integral F.ds where  F(x,y,z)=exsiny…

Q: Determine whether F(x, y) = xi +9yj is a conservative vector field. If so, find a potential function…

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Q: · Let F(x) = sin(4t²) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.69 Use this…

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Q: (2xy-tan(y))dx-(sin(y)ln(5x+15)-y^(-1))dy=0 using Exact Differential Equation

A: Given,Differential equation,2xy-tan(y)dx-sin(y) ln(5x+15)-y-1dy=0To find: General solution of the…

Q: se the divergence theorem to calculate the surface integral F · dS; that is, calculate the flux of F…

A: Given that Fx,y,z=xyezi+xy2z3j− yezk S is the region bounded by the coordinate planes and the planes…

Q: Complete the equivalent fraction: 25 5 ||

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Q: 5. Determine whether the follo (a) jst sin (x²) 27/2 da

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Q: Solve the given differential equation by undetermined coefficients. y" + y = 5x sin(x) 5.2 -x cos x…

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Q: The graph of f(x) is shown (see figure). 9x f(x) = = √√√x² + 7 (a) Find the following limits. L =…

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Q: QUESTION 15 Calculate the minimum value of 3x + 6y subject to the following constraints: x+y22 x +…

A: Given: A LPP, Min z=3x+6ysubject to,x+y≥2x+2y≤5x+y≤6x, y≥0 To find: Solution of given LPP.

Q: For each of the following, factor the matrix A into a product QDQT where Q is orthogonal and D is…

A: We can solve this using formula A= QDQT

Q: 5-7. D(x) = 2(x-3)² is the price, in dollars per unit, that consumers will pay for x units of an…

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Q: Х(и) 2

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Q: Evaluate the integral 1/F. F. dr. F(x, y) = = (5x² + y) i+ (3x − cos y) j where C' is the boundary…

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Q: Find the range for the function x²+y²=4

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Q: r = 6 sin 3r i - 6 cos 3t j O It is a parabola in the xy-plane, with vertex at the origin. O It is a…

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Q: Given the following graph, state (1) whether each edge is in the minimum spanning tree (MST) or not…

A: The graph given is as follows: (a) We are asked to check if the minimum spanning tree covers all…

Q: Consider the real sequence {an} given by Justify whether (a) it is an increasing sequence; (b) it is…

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Q: 02) Find the orthogonal trajectories for the family of curves given by x²y = k where parameter k is…

A: to find orthogonal trajectory we need to differentiate the equation and then replace dydxby…

Q: Evaluate the integral [yda+zdy – rdz along the helix C given by - X = = cos πt, y = sin ít, z = t…

A: Line integration of the vector valued fumction

Q: Consider the graph of f', the derivative of f, that is given below. Use it to answer the following…

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Q: d) ej Z [√2] is a field Z [√2] is an integral domain

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Q: Match the ordered pairs of integers on the left with the relation they belong to on the right.

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