2. For the given functions f (x), let.x, = 1,x, = 1.25, and.x, = 1.6. Construct interpolation polynomials of degree at most one and at most two to approximate f(1.4), and find the absolute error. a. f(x) = sin 7x c. f(x) = log,,(3x – 1)

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Q: Find Taylor polynomials of degree 4 at 0 for the functions defined as follows. ƒ(x) = (4+x)3/2

A: Find Taylor polynomials of degree 4 at 0 for the functions defined as follows.

Q: Q1: For the given function f(x)= sin 7 x, let x, = 1,x, = 1.25, x, = 1.6. Approximate f(1.4) by (1)…

A: Interpolation is the construction of new values using existing values where the arguments of the new…

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Q: the Taylor polynomials T₂(x) and T3(x) centered at x = 10 for f(x) = ln(x + 1). T. (m) 1

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Q: 8. For the given function f(x) = v1+x, let ro = 0, x1 = 0.6, and r2 = 0.9. Construct an…

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Q: Suppose that the first derivative of f(x) = is approximated by the following formula %3D 3x+4 -2f(x…

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Q: Which of the following would be expected to give the best approximation of f'(3) for f (x) = =…

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Q: 2. Suppose f (x)= log(tan(1+x)). The following values for f(x) are valid. f(1.00)=-1.456916, ƒ(1.05)…

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Q: For the given points X, = 1, x =1.5, x, = 2.5 and x, = 3. Find Lagrange Interpolation polynomial for…

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Q: 2. For the given functions f(x), let Xo 1,x 1.25, and.xy = 1.6. Construct interpolation polynomials…

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Q: Which of the following would be expected to give the best approximation of f'(3) for f(x) = sin(x)?…

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Q: Find Taylor polynomials of degree 4 at 0 for the functions defined as follows.

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Q: 4. For the given function f(x) = /2 + x², let xo = 0, x1 = 0.5, and x2 = 0.8. Construct a Lagrange…

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Q: 5. a) Find the second Taylor's polynomial P2(x) approximating the function f(x) = x + In (1+ x)…

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Q: 2. Show that for any p with 0.5 0 for the function f(a) = plog(1+ æ) + (1 – p) log(1 – a). -

A: We have used Maclarin series in the proof.

Q: 4. Suppose I give you the following function(x) = log,x and for the following *, = 3, x, = 9, x, =…

A: Interpolation is very useful in numerical analysis. An interpolating polynomial is a polynomial of…

Q: For the given functions f(x), let x, = 1,x1 = 1.25, and x, = 1.6. Construct interpolation…

A: PART A The given function is, f(x)=sin πx For x0=1 then f(x0)=0 For x1=1.25 then f(x1)=-0.7071 For…

Q: 1. For the given functions f(x), let xo 0, x= 0.6, and xy = 0.9. Construct interpolation polynomials…

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Q: The function f(x) = cos(3x) is interpolated on the interval [О, 1/5] with a polynomial of order 3…

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: For the given points Xo = 1, x =1.5, x, = 2.5 and x3 = 3. Find Lagrange Interpolation polynomial for…

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Q: 1. For the given functions f (x), let xo = 0, x1 = 0.6, and x2 = 0.9. Construct interpolation…

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Q: 17. The following values of the function f(x) = sin x + cos x, are given 10° 20° 30° flx) 1.1585…

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Q: For the given functions f(x)=sintx let xO=1,x1=1.25, and x2=1.6. Construct interpolation polynomials…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.