Find the formula 1 [ f(x) dx = w₁f (0) + w₁f (1) that is exact for all functions of the form f(x) = aeª + bcos (π²).

Q: 8. Suppose ao, a1, a2, ... is a sequence such that ao = a₁ = 1 and, for n ≥ 1, an+1 = n(an + an-1).…

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Q: Example 7.7. Find f (22) from the Gauss forward formula 20 25 30 35 40 45 f(x): 354 332 291 260 231…

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Q: 3. Find the general solution, given satisfies the complementary equation. As a byproduct, find a…

A: We can solve this using inspection

Q: Evaluate the following integrals. 4x+10 1. S dx (x-2)(x-1)²

A: Solution:  To find : ∫4x+10(x-2)(x-1)2

Q: u(x,y) with the constant c>1: Solution of this equation is A. u(x,y)=f(x+cy) B. u(x,y)=f(x-cy) C.…

A: Given PDE is ∂u∂y + c∂u∂x = 0

Q: /xy2. +xzu+yv2-3 = 0 The system of equations: |6x3y2 + 2xv - 3u²v2 - 5 = 0 - can be solved for y and…

A: Given system of equations xy2+xzu+yv2-3=06x3yz+2xv-3u2v2-5=0          .......(1) where x,u and v are…

Q: Evaluate the following expressions in MATLAB, where t = 8 s, i = √-1, and w = 1607 rad/s. (Enter…

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Q: Consider the so called Riccati ODE and let y₁ be a solution. y' = p(t)y² + q(t)y + g(t). Show that:…

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Q: 5. Residue theorem (a) +²+1 Jo° ±1 dt. +4+1 Use the residue theorem to compute

A: We have given integral∫0∞t2+1t4+1 We need  to use residue theorem to compute integral.

Q: Find the values of w,x,y and z in fraction form using a)gauss elimination, b) gauss-jordan…

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

Q: Example 7.31. Obtain the cubic spline for the following data x: 0 1 2 3 y : 2 -6 2 8

A: We have to find the cubic spline for the given data.

Q: Let f (x, y, z) be a function such that : (i) the function f (x, y, z) decreases most rapidly at the…

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Q: 5. A test has 28 questions that total 100 points. The test contains multiple choice questions that…

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Q: if the Positive root aso: ax²+x-1=0 it is calculated using the recurring formula X₁+1 = 1 = a (x₁)²…

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Q: Show that every covering of the Möbius strip is homeomorphic to either R², S¹ x R, or the Möbius…

A: We have to prove that every covering of the Mobius strip is homeomorphic to either R2or the strip…

Q: 4. Show the function f(2)=21m(z) is differentiable or not differentiable at any points.

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Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

A: We have to set up the integrals and then use the more convenient order to evaluate the integral over…

Q: List the eigenvalues of A. The transformation x→Ax is the composition of a rotation and a scaling.…

A: Solution

Q: Consider the plane P with the Cartesian equation 7x+ 5y + 5z = 33. (a) Express the above Cartesian…

A: Please type correctly

Q: Let C₁ be the circle r = 3 cos 0 and C₂ the cardioid r = 1 + cos 0. O (a) Find all point(s) of…

A: First, we have to find all the points of intersection of the two given polar curves. Then, we can…

Q: Match each of the following parametric Equations with a plane curve : x(t) = 3 + 5cos(t), y(t) = 4 +…

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Q: Suppose the invertible n x n matrices U and V satisfy the special properties U2 V2 and UVU = V. (a)…

A: Given : U and V are n×n matrices such that  U2 = V2  and   UVU = V. To prove : UmVUm = V  for all…

Q: 2 dy +4. dt d² y dt² +4y=2e¹

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Q: Find the equation of the line that passes through the point (-1, 3) and is parallel to the line 5x -…

A: Find the equation of the line that passes through the point (-1, 3) and is parallel to the line

Q: Evaluate the following integrals. 4x+10 1. S dx (x-2)(x-1)²

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Q: Let A (1,0, 2) and B= (6, -2,3). Solve for projAB. =

A: Given vectors are A = 1, 0, 2   and   B = 6, -2, 3

Q: 1. Solve each linear system below. Give a geometric interpretation of each system, by describing the…

A: Given system is 2x+y-z=10-----(1) -4x-2y+2z=-10-----(2) 2x-y+5z=3-----(3) (or)…

Q: A square matrix A is nilpotent if A" : = 0 for some positive integer n. Let V be the vector space of…

A: We shall solve first three subparts only as per the company guidelines. For others kindly post again…

Q: 13. Find the mass of a thin funnel in the shape of a cone z = √√x² + y²,1 ≤ z ≤ 4, if its density…

A: Here given the shape of a cone  z=x2+y2, 1≤z≤4 , Write it in polar coordinate D=r, θ: 1≤r≤4, 0≤θ≤2π…

Q: 6) Find the volume of the solid in the first octant bounded by the plane 3x +4z=12, y=2 and the 3…

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Q: y = cos(x) fonksiyonunun birinci mertebeden türevini x = noktasında h = olmakla ileri-fark yöntemini…

A: Given function is y=cosx. We have to evaluated the first derivative of y=cosx at x=π4 using the…

Q: The revenue of a company making the TV show "It's always sunny in Philadelphia" can be represented…

A: At break even total profit will be zero  To maximize total profit we can use calculus  For relative…

Q: procedure Horner(c, ao, a₁, a2, ..., an: real numbers) y := an for i:=1 to n y = y* c + an-i return…

A: Here follow the python code output.

Q: A study on the effect of remediation to the performance of students i mathematics. Descriptive…

A: we can give answer by using definition

Q: Question 12 The temperature T at a point (x,y,z) of a solid is given by the function T(x,y,z) = 2x²…

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Q: 3. Solve the diffusion problem that governs the temperature field u(x, t) a²uxx = ut, 0<x<L, 0<t<∞0…

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Q: The Wronskian of two differential functions f and g is W(f.g)=fg'-gf, more formally, f(x) W(f,g)(x)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: an In each of the equation below, find equation in rectangular coordinates. a) P+3=e b) r-2= 3020

A: A polar coordinate system contains a reference point and a reference direction. The reference point…

Q: 6. Solve the initial value problem y=-2y2 + ₁ + 2y₂ y = 2y₁ + 2y₁ - y₂ yı (0) = 1, y₂(0) = 0, y₁ (0)…

A: Given:   y"1 = -2y2 + y'1 + 2y'2 y"2 = 2y1 + 2y'1 - y'2 y1(0) = 1, y2(0) = 0, y'1(0) = -3, y'2(0) =…

Q: Industry Sectors Service Trade and Transporation Total sector United States Total Employment 68%…

A: Percentage change for Services: Percentage for 2010 is 68 and for 2020 it is 69% Hence Percentage…

Q: 1. If Alice uses the RSA modulus N = 77 and e=17, what is d? 2. Decrypt the message 5559 vising an…

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Q: Example 8.1. Given that 1.0 1.1 y: 7.989 8.403 dy find and dx (a) x = 1.1 (b)x= 1.6. d'y at dx² 1.2…

A: We need to make difference table to solve this problem. Please find step by step solution below:

Q: an In each of the equation below, find equation! a) P+3=e rectangular coordinates. b) r-2 = 3 cso

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Q: =H.w.2 Evaluate the following cartesian integrals by - changing them into equivalent Polar integrals…

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Q: X1 - 3Х2 - 4 X3 = 1 -X1 + X2 - 3x3 = 14 X2-3x3=5

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Q: (a) The dimensions of the rectangular block are 10cm by 20cm by 15cm. with a possible error of 0.05…

A: We have to find (approximately) the greatest error in the surface area of the block and the…

Q: Solve the differential equation below using series methods. (-7x²+8)y'' - 2xy = 0, y(0) = 4, y'(0) =…

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Q: Solve using Laplace transforms y''+2y'-6y=7e-3t, where y(0)=1, and y'(0)=-2

A: Solution

Q: 5. Winona asks her math teacher how many multiple choice and free response questions will be on the…

A: Given is some information about Winona.   To Write: A system of Linear Equations and use matrices to…

Q: 3. Suppose y(t) is the inverse Laplace transform of the following function: y(t) = L-1 What is lim…

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