Construct piece-wise linear polynomials for function f(x) = over the interval (0,0.4] with h= 0.2. Estimate the number of subintervals to use with piece-wise linear interpolations such that the error is within 104. Construct piece-wise quadratic interpolations for f(r) over (0, 0.4] with 4 subintervals.

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: Interpolate the function f(x) = ev3 on [-1, 1] with a second degree polynomial by using the zeros of…

A:

Q: Determine the Tntervals Where the function f(x) = 3x4-6x² Is incieasing decleasina or

A: Consider the given function fx=3x4-6x2. The problem requires to determine the intervals in which the…

Q: Find an expression for the nth Maclaurin polynomial using sigma nota- tion for the function cosh x.

A: Suppose f has n derivatives at x=0 then nth Maclaurin polynomial of f is pn(x) where pn(x)=∑k=0n…

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: 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: Find the Taylor polynomial of degree two approximating the given function centered at the given…

A:

Q: Find the polynomial that interpolates the function Vx at points x = 2,3,4 and 6 with cubic…

A: We will use Lagrange's interpolation method to first find the polynomial and then the approximation…

Q: Calculate the error in using the divided differences for approximating the derivative at x 5 using a…

A: Use the Newton's divided difference interpolation formula, to obtain the equation for f(x).…

Q: Find all the of the polynomial function f (x) = x° - x - 1 at ro = 1.5 at 5th iteration using…

A:

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

A:

Q: Use Divided difference method to construct a second degree polynomial P2(x) to approximate f(x) = e…

A: Newton's Divided Difference Interpolation formula is…

Q: Find a cubic polynomial with a critical point at x = 2, and inflection point at (1,4), and a leading…

A: Find a cubic polynomial with a critical point at x = 2, and inflection point at (1,4), and a leading…

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 Maclaurin polynomial approximation of degree n for the function f(x)= e2x , and write a…

A: Maclaurian polynomial: The Maclaurin polynomial approximation of degree n for  the function f(x) is…

Q: ) Find the Taylor polynomial p2 for f(x) = at x = 2. x3

A:

Q: Obtain a quadratic polynomial approximation to f (x)= 3e* using Newton divided difference…

A: Given:        f(x)=3ex       Here h=b-aN                  =0.5-04=0.125     The value of table for x…

Q: 2. Will the limit of all polynomial functions / (x) as x approaches a be always equal to the value…

A: Find your answer below

Q: Find the interpolating polynomial of degree two for f(x) cos(r2) +r on the interval [-1, 1] using…

A:

Q: The 2nd degree polynomial that interpolates to f(x): = 2cosx - sinx at x = 0, x = π/2 and x = π is…

A:

Q: Q4) Find the root of f(x)= (x^2)-5, in interval [0,4] by using bisection method.

A:

Q: If f(x)=ln(x) and x,-3.1, x₁-3.2, x-3.16, then the error bound in Lagrange interpolating polynomial…

A: Given the function is fx=lnx and x0=3.1, x1=3.2, x=3.16

Q: According to the Table below calculate the function value at x = 2: a) by using Linear Interpolation…

A: The given table of values is

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: 3. Use Lagrange interpolating polynomial of degree 4 to estimate f(1.9). 0.5 1.2 1.7 2.1 3.0 f(x) 1…

A:

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: Consider f(x) e on [0, b] and its approximation by an inter- polating polynomial p2(x) at the evenly…

A: Given that f(x)=ex on [0,b]We have to approximate the above function in [0,b]i.e…

Q: estimate the value of x correspond to f(x) = 1.6 Using cubic interpolating polynomial together with…

A: Given data is x 1 2 3 4 f(x) 3.6 1.8 1.2 0.9 The value of x corresponding to f(x) = 1.6…

Q: . Suppose that f is a polynomial of degree 1 and s1, is the linear spline that interpolates f at the…

A:

Q: Find the first order polynomial of variable x "closest" to the polynomial x2 + 3x + 1 using the…

A:

Q: Express p(x)= x3 as a Taylor polynomial about a = -1.

A: The Taylor polynomial of degree n about  is given by:f(x) = f(a) + f'(a)(x-a) + f''(a)2!(x-a)2…

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

A:

Q: Compute the interpolating polynomial through the points (–1, 5), (1, –3), (3, 21) using the…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: Determine the third order MacLaurin's polynomial for f(x) = ex.

A: Given,  f(x)=ex

Q: Find Newton’s polynomial that interpolates f(x) = x1 at x = 1, x=2,x=4,andx=5.…

A: Since, function is not clear so we assume fx=1x. We have to find the Newton's polynomial that…

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

A:

Q: Determine all Taylor polynomials for f(x) = x^2 + 2x + 1 atx = 0.

A: Given: fx=x2+2x+1 x0=0

Q: 2. Construct the Lagrange interpolating polynomial of order at most two P,(x) of f(x) using the…

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: 4. Expand f (x) = 1 around a = 0, to get linear, quadratic and - 1-x cubic approximations.

A:

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: Estimate√16.2 using the linearization L(x) of f (x) =√x at a = 16. Plot f and L on the same set of…

A: To Determine: Estimate√16.2 using the linearization L(x) of f (x) =√x at a = 16. Plot f and L on the…

Q: The polynomial 1 + x + x²/2 is used to approximate f(x) = e*. Use the Remainder Estimation Theorem…

A: The polynomial 1+x+x22 is used to approximate f(x)=ex. Since we know that Taylor expansion for the…

Q: is a polynomial O has repeated roots at x = 0 O has a slope equal to zero at x = 0 O is always…

A:

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

A:

Q: Use the error bound for SN to obtain another proof that Simpson’s Rule is exact for all cubic…

A: