Find the interpolating polynomial to the function f (x)= In(x +1)+sinx at x – 0, 1, 2, 3, 4, 5 using: (i) Newton forward interpolation formula (ii) Newton backward Interpolation formula Draw the graphs of the original function and the interpolating polynomial and mark the error with color.

Q: 4. Use the Newton's Divided Difference formula to compute the cubic interpolating polynomial for…

A: To find- Use the Newton's Divided Difference formula to compute the cubic interpolating polynomial…

Q: Q-2. Determine the values of x for which the function J (X) =$in Xcan be replaced by the Taylor 3…

A: We have to find the value of x as per given conditions.

Q: a) Calculate f(3.4) using Newton's interpolating polynomials of order 1, 2 and 3. All numeric values…

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Q: Determine the interpolating polynomial in Newton's form that passes through the points and Use the…

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Q: (a) Differentiate the Maclaurin polynomial of degree 3 for f(x) = sin(x) and compare the result with…

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Q: Let g (x, y) = 9 sin(xy) – 11x² In(y) + 4. Find the degree 2 polynomial, p, which best approximates…

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Q: Find the interpolating polynomial of the following point and function using Newton's interpolation…

A: We are entitled to solve only one question at a time only, so we will answer only the first…

Q: determine the degree of the maclaurin polynomial required for the error in the approximation of the…

A: f(x)=cosxLet f be a real valued and differentiable function through n+1 order in an interval I…

Q: The equation for the maximum deflection as a function of x is given by: -0.67665x10x -0.26689x10x³…

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Q: tion 10 Jsing Newton's backward difference polynomial of degree 2, for the below data, approximation…

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Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of the…

A: The given function is f(x)=cosx To be approximated at x =0.4 formula used: Rnx=fn+1xn+1n+1!

Q: Approximate f(x) = secx by Taylor polynomial with a degree of 2 at x = 0. What is the accuracy of…

A: Taylor Series approximation:  And Error Bound

Q: 15) Use Lagrange interpolating polynomial to derive a two points forward formula to estimate f'(xx)…

A: To find :  15) a two points forward formula to estimate f'x0 using Lagrange interpolating polynomial…

Q: Find the Maclaurin polynomials Tn for f (x) = cos(x2). You may use the fact that Tn(x) is equal to…

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Q: 11. a. For the function f(x) = (3x+2), let x, =-1, x, =0, x, =1. Construct interpolating polynomial…

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Q: 2. Find the Maclaurin polynomial of f (x) = cos x.

A: Using maclaurian series of polynomials,

Q: Find the seaond Lagrange înterpolation polynomial that n ercepts f(x)= x²+xe*+sinx at points…

A: NOTE: A and B are not subparts of the given question, they are options and we have to choose the…

Q: Let p be a polynomial of degree n and let  S = { x is an element in interval (0,pi/2) | cos(x) =…

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Q: Find the local quadratic approximation of f at x = x0, and use that approximation to find the local…

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Q: Using equally spaced nodes on the interval 0, 0.3. the upper bound for the error of the cubic…

A: For the cubic interpolating polynomial. Take x0,x1,x2,x3 Hence,to find h h=b-a3=0.3-03=0.1 Error is…

Q: Determine the area, in square units, bounded above by f(x)=−x^2−8x and g(x)=3x+24 and bounded below…

A: Given that  fx=−x2−8xgx=3x+24 To find the area bounded above by f(x)

Q: Use the numbers x, = 2 , x, = 3 and x, = 4 to find the second Lagrange interpolating %3D polynomial…

A: First of all we have to find the second Lagrange interpolating polynomial for f(x)=1/x Then we have…

Q: Find the interpolating polynomial of the following point and function using Newton's interpolation…

A: according to our guidelines we can answer only first question and rest can be reposted.

Q: Use the Linear Approximation to estimate Af for f(x) 5+x2 when a = 2 and Ax = -. (Use decimal…

A: Given :   f(x) = 11  / 5+x2     a = 2     ∆x = - 1/2 = -0.5

Q: Let F(x) = || sin(8t²) dt. %3D Find the MacLaurin polynomial of degree 7 for F(x).…

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Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of the…

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Q: (B): For the function f(x) sinx, let x, = 0, x1 = 0.6, x2 0.9.Construct Lagrange polynomial %3D…

A: Given fx=sinx, x0=0, x1=0.6, x2=0.9. The lagrange polynomial interpolation of order 2 for a function…

Q: The value of the function f(x) and some order derivatives at the point x=1 are given in the…

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Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show…

A: We will find out the required value.

Q: 2. y = cos ( 2x ) at x = [0,r] with four equally spaced points. %3D

A: The interpolation techniques are used to establish the functional relationship between any two…

Q: Find the second Lagrange înterpolation polynomial that rn tercepts flx)= x²+xe*+sinx at points xo=0,…

A: We have to find the second-order Lagrange interpolation polynomial that interpolates fx=x2+xex+sinx…

Q: Formulate the required Newton's form of the interpolating polynomial for the given function using…

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Q: Find out the Lagrange interpolating polynomial of the first, second and third order to evaluate…

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Q: Using legendre Polynomials, Find a quadratic last squares approximation to f(x) = cosh (X)

A: Using Legendre polynomials, We have to find a quadratic least-squares approximation f(x) = cosh(x).

Q: Find the interpolating polynomial of the following point and function using Newton's interpolation…

A: Please check step 2 for the solution.

Q: From the table find f(1) using interpolating of Lagrange polynomial -102 Y=f(x) 2 -1 5 1 O -1 O о о…

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Q: for the function f (x) = x + . Estimate a) Lagrange interpolating polynomial b) Newton's…

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Q: Let f(x) = x2 – 6 and po = 3 and pi = 2. Use Secant method Example: to find p3.

A: Given: f(x)=x2-6, p0=3 and p1=2 To find: Value of p3 using Secant method.

Q: Determine the values of x for which the function can be replaced by the Taylor polynomial if the…

A: Please see the white board. f(x) is approximated by the polynomila of order 3.The error term En(x)…

Q: Find the best upper bound for the error when using Newton polynomial p3x to estimate f(x)=ln(x+2) in…

A: Given: f(x) =ln(x+2)  over the interval  [0.1, 0.4]

Q: 2) Find the 3€ Tayler polynomial P,(x) fix) = Sinx at X= -½. 3) Using B,(x) from 2), estimake sin…

A: The formula for taylor series is     where f (k) (a)  is kth derivative of f at given point a.

Q: Let g (x, y) ) = 11 sin(xy) — 13x² ln(y) + 20. Find the degree 2 polynomial, p, which best…

A: Given: The function is g(x,y)=11sin(xy)-13x2ln(y)+20 To find: The degree 2 polynomial which best…

Q: Use Newton.s interpolating polynomial to determine y at x= 8 to the best possible accuracy. 1 2 5.5…

A: Given data is  To find the value of y at x=8 using Newton's interpolation formula,

Q: Let f(x)=x-4x2. Find the polynomial that interpolat es f at points x0=-2 , x1=0, x2=1 and x3=2 using…

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Q: A scientist has executed one experiment to identify the values of an unknown function f(x). The…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Show that a nonzero polynomial function y = f(x) cannot sat- isfy the equation y" = -y. Use this to…

A: given equation is  y"=-y

Q: 1. Use the numbers x, =1 , x, = 2 and x, = 3 to find the second Lagrange interpolating polynomial…

A: We have x0=1, x1=2, x2=3 The polynomial is fx=x-2=1x2 Therefore,…

Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to…

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Q: The function f(x) = cos(3x) is interpolated on the interval [0, 1/5] with a polynomial of order 3…

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