11. a. For the function f(x) = (3x+2), let x, =-1, x, =0, x, =1. Construct interpolating polynomial to approximate f(0.5). b. Find an error bound for this approximation.

Q: " + 4x' + 4x = 4e24, r(0) = 0, r' (0) = 1.

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Q: Written assignment 1: Prove Proposition 6.39: Let n EN such that n> 1. Then n has a prime factorizat...

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A: To find solution of the differential equation: y2y''=y' 

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Q: Liam makes fruit punch by mixing orange and pineapple juice 120 ml of orange juice 320 ml of pineapp...

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Q: C. Find all complex numbers z of the form 2=x+y such that that zz = 25 and *+y = 7.

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Q: Don't use calculator to solve.

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to approxi...

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Q: Determine the solution of the first-order ordinary differential equation: 2y' +4y- 4y cos x 0

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Q: 1+ax dx Evaluate log 1-ax x 1-x

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Q: Given the differential equation: (x +16)y"+ +2y = 0 The singular points are: 3 3,4,-4 This option Th...

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Q: 4n+1 Σ 32n n2 n=1

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Q: Using dot and cross products only, show which of the following vectors are perpendicular and which a...

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Q: 2. Let the rref of a matrix A be, (1 0 2 0 -2 0 1 -5 0 -3 0 0 0 1 6 Determine A if the first, second...

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Q: 5. Find the general solution to the differential equation e-y" = (y')? (where y' = ) dx

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Q: 5) Use improved Euler method to find y(2) if y(1)=2 for dy xy!/3 %3D dx take h=0.5

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Q: 14. F(t) = 27,0st<3; F(t + 3) = F(t) %3D %3D 15. F(t) = {.0<t< 4

A: Note : " As per our guidelines we will solve the  first question . If you want any specific question...

Q: 4. Use the Laplace transform to solve the IVP r" + 4x' + 4x = 4e2", a(0) 0, r'(0) = 1. %3D

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Q: Let V = R?. For (u1, u2), (v1, v2) E V and a €R define vector addition by (u1, u2) H (vı, v2) := (u1...

A: From the given formula of the vector addition, it is obtained that u1, u2⊞v1, v2=u1+v1+3, u2+v2-3. S...

Q: dy Q1: = x+ y?, y(0) = 1 , find y at x = 1 use h 0.2 (use Modified Euler dx Method)

A: To find y at x=1 by using Modified Euler's Method. 

Q: Use polar coordinates to find the limit. [If (r, 0) are polar coordinates of the point (x, y) with r...

A: We have ,  f(x , y) = 4e-x2-y2 - 4x2 + y2 By using polar coordinates , plug x = rcosθ  , y = rsinθ T...

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A: A basis {u,v,w} is said to be  Orthogonal basis if, u.v=0 , v.w=0 , w.u=0. Orthonormal basis if u.v...

Q: Find the probability that either a 6 or 7 will be obtained in one toss of a pair of dice.

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Q: 5. Prove the following identity for n 2 1: Fzn+1 = F+1+ F;

A: We need to prove that ,  F2n + 1 = F2n+1 + F2n We know that ,   Fm+n = FmFn+1 + Fm-1Fn ,  m ≥ 1 , n ...

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Q: 3 Evaluate the determinant for the following matrix: 1 O A.8 ОВ. -2 О С.5 O D. -4

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Q: Express the integral LL fEy,2) dzdxdy a as an iterated integral in the other five different ways.

A: To find the other iterated integrals we have to change the orders of the integration. 

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Q: Let x be a continuous random variable that is normally distributed with mean u = 26 and standard dev...

A: This is a problem of Normal Distribution.

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Q: 2. Using the identity -4 %3D 5 compute -6 -5 Hint: = I2 2

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Q: СВ

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Q: | (r log x)² dz,

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly rep...

Q: Q3: Use Euler's Method to find a numerical solution of the differential equation dy y = 3 + dx With ...

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Q: Q3/ find the general solution of the following PDE yzx – xz, + x2 –- y? = 0

A: The given PDE can be written as  yzx-xzy=y2-x2  

Q: QUESTION 3 Find f(t) -3s +(| )(t- f(t) =

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Q: 5. Prove that if a matrix A is invertible and diagonalizable, then matrix A-1 is also diago- nalizab...

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Q: Compute for the determinant using cofactor expansion 41 2 2 7 1 2 -2 6 6 -6 13 14 [-2 2 -6 1] O -200...

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Q: P with equation 2x – 3y = 0. Sketch the graph of P. 3. Determine the focus and directrix of the para...

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Q: OFind a root of an equation f(x)=2x-2x-5 using Newtor aphson Method

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