Given that xo= -1 and x1= 1. Then the basis of the first Lagrange polynomial Lo(x) and L,(x) are respectively Select one: a. 0.5+0.5x and 0.5x-0.5 b. 0.5-0.5x and 0.5x-0.5 c. 0.5-0.5x and 0.5x+0.5 d. 0.5+0.5x and 0.5x+0.5

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A: Given, if q(x) is an arbitrary polynomial in Pn it follows that                   q(x) = c0p0(x) + .…

Q: Determine the third Taylor polynomial of the function at x = a. f(x) = x 2 + x+1, a = 4

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Q: If we multiply the Legendre polynomial of degree n by an appropriate scalar, we can obtain a…

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Q: Find all homogeneous polynomials of degree 3 in R² 3 p = Ax² + Bx²³y + Cxy² + Dy ³ that are…

A: Let, the homogeneous polynomial beThen, the function p is called harmonic if

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Q: the error estimate for Taylor polyno

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Q: The coordinates of the P(x)=x³ – 2x2 + 3x polynomial with respect to the base B-[1, x, x?,x'] are as…

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Q: Find the Taylor polynomial T3(x) for the function f centered at the number a. f(x) %3D хе 4х, а%3D 0…

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Q: 6. Let 1 f (x) - cos x + sin(2x), x E [0, 1] 2 Find the least squares polynomial approximation of…

A: Let fx=12cos x-sin2x, x∈0,1. To find quadratic fitting  fx≈P2x=a0+a1x+a2x2 Consider, s0=∫011dx=1

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Q: Find the third degree Taylor polynomial centered at c = 1 for the function. f(x) = √√x Select one: O…

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Q: Q4) Consider the Lagrange coefficient polynomial L2x(x) that are used for quadratic interpolation at…

A: The Lagrange coefficient polynomials are given as,…

Q: Find the degree 2 Taylor polynomial of f(æ) 1 at a = 0. x + 2 O 1 x2 2 4 8 O 1 x2 4 4 O 1 x2 2 4 8 +

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Q: Consider the polynomials a(x) = r' + x³ + x + 4 and b(x) = 2r³ + 4.x² + x + 2 from Z5[r]. a) Find…

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Q: The function f(x,y,w)=√6xy+5w^2-x^2-0.5y^2-4y+7 has a unique stationary (i.e., critical) point. Find…

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Q: that the Lagrange Polynomial of values Know follows b) F a) T as 0 1 2 = (x²-19x + 6) :- 3 7

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Q: Calculate the equation of the second-degree Taylor polynomial using the following formula: dg dg…

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Q: A function S is defined on the interval [-1,3] by S₁(x), xЄ[-1,0), S(x) = S2(x), xЄ [0,2), S3(r), x…

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Q: (1) Let ao = 0, a1 = 1, am = 3a,-1+ 10am-2 + 14 - 5" Find the solution of a, using the…

A: Given: a0 = 0 , a1 = 1 , an = 3an-1 +10 an-2 + 14·5n To determine: (a) The solution of an, using the…

Q: 1: On the polynomial space P₁ John chooses the scalar product (flg)₁ = ₁f(x)g(x) dx, while Jim uses…

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Q: 2. Consider the Newton polynomial Pn(x) = ao+a1(xr-xo) + a₂(x-xo)(x − x₁) +... +an(x-xo)(x -…

A: Given that   that interpolate then we have Now  ,       putting

Q: Let z E (-1,0) and let R. (z) be the remainder in Maclaurin's formula for In(1+2) in Cauchy's form.…

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Q: In linear space, consider all true polynomial functions with internal multiplication x(t)y(t)dt for…

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Q: The position function of a spaceship is 4 t² + 1 and the coordinates of a space station are (8, 4,…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.