Q2. Consider Xi 0.12 yi 0.7917 0.7733 0.7437 0.24 0.36 0.48 0.7041 0.6563 0.6023 0.60 0.72 Using Newton's interpolating polynomials of order а) 1 b) 2 c) 3 to estimate the function for x = 0.40.

Q: let f(x)=ex for 0 < x < 1 Approximate f(0.25) using linear interpolation with x0=0  and x1=0.5 .…

A: Substitute x0=0 and x1=0.5 in fx=ex  and calculate L0(x) and L1(x), to construct the Lagrange…

Q: (a) Find if y = - (In z)*". (b) The function f(x) = (In z)* is an invertible function (you do not…

A: Given query is to find the derivative of the expression.

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

A:

Q: From the given data, identify f(4) using Lagrange and Newton's polynomial. (2,10), (3,15), (5,25),…

A: The Lagrange and Newtons polynomials can be used to find a polynomial for the given set of data.…

Q: Let f(æ) = VE = ai. For æo = 2.6, #1 = 3.4, x2 = 3.9, 23 = 4, æ4 = 4.5, %3D • What is the maximum…

A: Given function is f(x)=x13 and points are x0=2.6,x1=3.4,x2=3.9,x3=,x4=4.5 So corresponding function…

Q: Consider the function f(x) = x³ + 2x + 5. 1. Estimate the root to two significant digits using…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: 1. Use bisection method to find a root of f(x)=x^3 -3x^2-6x+8=0 near x=3.5 2. Use Newton's method…

A: 1. we need to find a solution of f(x)=x3-3x2-6x+8=0 near 3.5 by using bisection method Now let us…

Q: 5. Find the polynomial P2(x) that approximate the function Ax)=sin(x) over the interval [0, 7/2].…

A: Here we use Newton's Divided Difference.

Q: 2. Find the Maclaurin polynomials of order n=0,1,2 for f(x) = cos(x).

A: Consider the formula for Maclaurin series: Calculate the derivatives to find the terms in the…

Q: For the f(x) = Vx +1 let construct interpolation polynomials by Newton Backward-difference method to…

A: NEWTON BACKWARD DIFFERENCE FORMULA: Let f(x) be the function of variable x and let h be the…

Q: 2. Give the table below: * 1.0 | 1.2 1.4 1.6 | 1.8 f(x) 0.23 0.34 0.45 0.58 0.63 Use Newton forward…

A:

Q: 1. Determine the discrete least squares trigonometric polynomial S2 (x) on the interval [-T, 7] for…

A:

Q: Q2. Use the Newton Backward interpolation formula to compute f (-0.92) from the following data. -2.0…

A:

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

A:

Q: Differentiate the function L(k) = cosh¯' (/T+ k² ). O (k² + 1)-1/2 O 1+ k2 1+k

A: ddkcosh-11+k2

Q: 12: Apply Newton's method with line search for f(x) = x₁-x2 + 2x² + 2x₁x₂ + x2 with a starting point…

A: We have f(X) = x1-x2+2x12+2x1x2+x22

Q: Suppose that p(t) is a differentiable function with $'(1) S kø(1) (k > 0) for 1 2 a. Multiply both…

A: Given: Suppose ϕ(t) is a differentiable function with ϕ'(t)≤kϕ(t) (k&gt;0) such that ddtϕ(t)e-kt≤0.…

Q: Consider the function f(x)= x³ + 2x + 5. 1. Estimate the root to two significant digits using…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: (2) The real part of Syy (@) and the real part of Syx (@) are even functions of o, i.e., Re[Sy (@)]…

A:

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: 3. (a) Consider the following dataset. Compute the value of f(x) when x=6 using 2nd order Newton…

A: Given, i 0 1 2 3 xi 2 4 5 8 y=f(x) 0.693 1.386 1.609 2.079 First of all we will calculate…

Q: From the Newton's Interpolating function, estimate the function at x₁ = 3m using Forward, Backward,…

A:

Q: (a) Develop a table of f(x)=2e* + 3x for x = 3, 5, 7 and 9. (b) Estimate f(4.2) using the…

A:

Q: Q2: Use a Newton-Gregory polynomial (Forward & Backward) of degree 3 that fit table below, then find…

A:

Q: 5. Use Green's Theorem to evaluate f. $ (y² – 4x) dæ – (2+ x²y²) dy where C - - is shown below. y…

A:

Q: what is the approximate value at point x- 0.7 of the interpolation polynomial obtained using the…

A: We have the following values: x y -1 4 0 11 1 16 2 13 Now, let make the backward…

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

A: Consider the given function. fx=x+ln1+x (a) We have to find the second-order Taylor polynomial about…

Q: 5. Let f(x, y) = 3xr² + xy- y. (a) Compute f(1.02, 1.99) exactly. (b) Let f(1.02, 1.99) = f(1+0.02,…

A:

Q: 2. Give the table below: 1.0 1.2 1.4 1.6 f (x) | 0.23 0.34 0.45 0.58 0.63 1.8 Use Newton forward…

A:

Q: Let f(x) = Q[x] be a irr of prime degree p. If fr non-real roots then th

A:

Q: 5) Find the velocity of rocket by using Gregory-Newton interpolation polynomial at t=260 sec. time…

A: Consider the given table. We have to find the velocityt=260 sec Since, t=260 sec is near to the…

Q: a) Develop a table of f(x)= e¯* + 5x for x = 2, 4, 5 and 8. b) Estimate f(3.2) using the…

A:

Q: Compute f(0.25) from the following data using Backward Gregory – Newton Interpolation Formula (BGNIF…

A: Function curve can be plotted by plotting the data points and joining the data points by smooth…

Q: 2. if √o = √T = 1 and √4 = 2 estimate √3 to by constructing Lagrange polynomial, then compare with…

A:

Q: 2. Consider the data: X 0.1 0.2 0.3 0.4 0.5 f(x) | 1.40 1.56 1.76 2.00 2.28 Use the Newton's forward…

A:

Q: Construct a Lagrange interpolating polynomial to approximate u at the temperature of 38°C. Use your…

A: Given:                                     To find: Lagrange interpolating polynomial to…

Q: 11) Find the best upper bound for the error when using Newton polynomial P3(x) to estimate f(x) =…

A: Concept: The upper error bound using the newtons polynomial: Rn≤Mnn+1!maxx∈a,bx-x0x-x1....x-xnWhere…

Q: 3. Find the lincar approximation of the function g(x) = V1+x at a = 0 and use it to approximate the…

A: Use taylor form

Q: Calculate f (3.4) using Newton.s interpolating polynomials of order 1 through 3 and estimate the…

A:

Q: A particular finite difference formula for the first derivative of a funtion is: f '(xi) =…

A: Given: f'(xi)=-fxi+3+9fxi+1-8fxi6h, where xi, xi+1, xi+2 and xi+3 are equally spaced with step size…

Q: Use Müller's Method to determine all the roots of f(x) =x' – x – x-2 Choose x2=1.0, Xo=X2+dx2,…

A:

Q: Consider the function f(x) = x³ + 2x + 5. 1. Estimate the root to two significant digits using…

A: Given, fx=x3+2x+5 We have to find the root of fx in the interval -1.4, -1. In bisection method, if…

Q: Q3. Prove that if g interpolates the function f at ro, T1, . .. , In-1 and if h interpolates f at…

A: We have to prove that if g interpolates the function f at x0,x1,…,xn-1 and if h interpolates f at…

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: Find the second Lagrange înterpola tion polynomial that fn ercepts fl(x)= x+xe*+Sinx at points xo=0,…

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

Q: 11. Suppose that f'(x) = Vx² + 5 and f(2) = -4. (a) Use the linear approximation of f at x = 2 to…

A: The given question can be solved as shown in step2.

Q: A. Compute the bound B of the error when approximating f(x)=sin(x) with a polynomial of degree 1 in…

A: The given function is fx=sin x. Find the error bound for f approximating with a polynomial of degree…

Q: (a) The following data is giwen about a certain function 1 12 14 16 18 20 0 0 1823 0 3365 0 4700 0…

A: Given :-  The following data is given about a certain function : xi 1 1.2 1.4 1.6 1.8 2.0 f xi…