28. The Lagrange's interpolating polynomial for 3 4 f(x) 8.

Q: 3) Compute the Maclaurin polynomial of degree 4 for the function f(x)=cos(x) In(1-x) for -1<x<l.

A: Consider the given function f(x)=cosxln1-x   ; -1&lt;x&lt;1 The formula to find Maclaurin series,…

Q: 13. From an experiment, we get the following values of a function O(x). 1 2 -4 f(x) 3 -5 4 Represent…

A:

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: Find the Taylor polynomial T2(x) for the function f(x) = 4e³x at x = 0. (Use symbolic notation and…

A: Solution

Q: (10) 3 f(-1) = 1, f(1) = f(0) = 4, and f(r2) = f(1) = 1, to construct interpolating polynomials of…

A:

Q: Q3) Find the Lagrange polynomial that fits the followin value of y at x-0: Ans. y-6.03888 -2 3. 5.…

A:

Q: Find the the Taylor's polynomial P2(x)for the function f(x) = 5x2e-2 about xo = hence find f(0.5).…

A: Given, f(x) =5x2e-2xThe Taylor's polynomial P2(x) about x…

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

A:

Q: 10) Find the cost of evaluating p2(x), for a specific x, where p2(x) is the Lagrange interpolating…

A: The cost of p2 (x) for a specific value of x will be given by following formula-

Q: O is Cos x about x The second-degree Taylor polynomial for f (x) = 1-x

A: The second degree Taylor polynomial of a function f(x) at x=a is given by…

Q: 3. Produce the linear and quadratic Taylor polynomials for f(x) = Vx, a = 1. Graph the function and…

A: Definition used -                 Taylor polynomial for function f(x) at x = a is given by -…

Q: 9) Find the cost of estimating f(x) using Lagrange interpolating polynomial p2 (x) for a specific…

A: To find: Cost of estimating fx¯ using Lagrange interpolating polynomial P2x for a point x¯. We shall…

Q: , Consider the interpolating polynomial for f(x) =x² based on th points (0,0). (1,1) and (2,8). Find…

A:

Q: Find the Taylor polynomial p5 for f(x) = 3 ln(x) at x = 1. Sorry, that's incorrect. Try again?

A:

Q: 4- By using Lagrange polynomial the vahue of f'(3) from the following table is 52 2 4 112 f(x) -2 F…

A:

Q: Q4. Use Newton forward-difference formula and construct appropriate interpolating polynomial and…

A:

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

A:

Q: Consider the function f(x) = 3 sin (). Construct the interpolation polynomial which interpolates the…

A:

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

A: Given function is f(x)=x2esinx+ln(sinx) Find 'f(x)' corresponding to given values of 'x' x 1 1.5…

Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

A: Sol

Q: 1) Let f(x) = e2* Find 3rd Maclaurin Polynomial for f(x)

A: Given f(x)=e2x To find the third order maclaurins polynomial

Q: If f(1) = 2 and 3 <f'(x)<5, what is the largest f(4) can be? Be sure to fully justify your work. In…

A:

Q: 1 (Ь) Now consider f(x) Find the error if we were to use the third degree Taylor V4 + x 1 Make your…

A: Given that, the function is fx=14+x, entered at 0. Find the value of f0 as follows, f0=14+0=14=12…

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

A: In this question we have to find the interpolating polynomial by using Newton's interpolation…

Q: 3/2 Construct the fourth degree Taylor polynomial at x= 0 for the function f(x) = 3(1 - x)2. P4(x) =

A: Solved below

Q: sin

A:

Q: Let g (x, y) = 7 sin(xy) — 9x² ln(y) + 8. Find the degree 2 polynomial, p, which best approximates g…

A:

Q: Let f (x) be a function whose Taylor polynomial of degree 4 about x 2 is given by P(x) = 2 + 3(x 2)2…

A:

Q: 1. Using x, = 1,x1 = 2,x2 = 3, and x3 = 4, find the Lagrange interpolating polynomial of In(x + 1).

A: Given function is f(x)=ln(x+1) Evaluate value of function at given set of points: x 1 2 3 4…

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

A:

Q: 7. a) Use the appropriate Lagrange interpolating polynomial of degree two P,(x) to approximate…

A: Given f0.1=0.665, f0.2=0.8, f0.3=1.8, f0.4=0.25

Q: t is known that the polynomial p(x) = 2- (r+ 1) + x(x+ 1) – 2x(r + 1)(r – 1) interpolates the first…

A: Given:- p(x)=2-(x+1)+x(x+1)-2x(x+1)(x-)  interpolates the first four points of the table. x -1 0…

Q: If the polynomial P(r) is the nth Taylor's polynomial for f(r) about the point zo then the upper…

A: Given: If the polynomial pnx is the nth Taylor's polynomial for fx about the point x0 then the upper…

Q: Construct lagranges interpolating polynomial of atmost degreee2 to approximate f(2.3) from the table…

A:

Q: = -5. Let p2(x) be the interpolating polynomial of f(x) at xo = Then, the error term in…

A:

Q: 10) Use Lagrange coefficient polynomial L3,2(x) to find L3,2(5) using the nodes Xo = 3,x1 = 4, x2 =…

A:

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…

A:

Q: 4) Polynomial of lowest de 1) and with f (0) = -18

A:

Q: 1. Find the Maclaurin polynomial of degree 4 for the function f(x) = Vx+ Answer:

A: I am going to solve the given problem by using some simple calculus to get the required result.

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: The Lagrange polynomial that passes through the 3 data is given by 15 18 22 y 24 37 25 2 (x) = 24L1…

A: The three point interpolation formula through the points x0, y0, x1, y1, x2, y2 can be defined as…

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

A: Given: The function is  f(x)=x2esin x+ln(sin x) The points are x0=1, x1=1.5, x2=2.5, x3=3   To…

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: 1. For the function f(x) = /1+x, let ro = 0, x1 = 0.6, and r2 = 0.9. Con- struct Lagrange…

A: Given:

Q: 3 Let f be a function with third derivative f (x) = (4x + 1) 7. What is the coefficient of (x – 2)*…

A: Explanation of the answer is as follows

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

A: Given: g(x, y) = 9sin(xy) -11x²ln(y) +4 To find: Taylor Polynomial of 2nd degree   Dear student,…

Q: To find an nth Lagrange interpolation polynomial p(x) we need n distinct numbers and their values in…

A: To find an nth Lagrange interpolation polynomial p(x) we need n distinct nbers and their values in…

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 Taylor polynomial T2 (x) for the function f(x) = 2es* at x = 0. (Use symbolic notation and…

A:

Q: (a) The nth Maclaurin polynomial pn(x) -x* of a (n times differen- k! %3D k=0 tiable) function f(x)…

A: A Maclaurin polynomial (Taylor polynomial at 0) expansion is given by,