what is the approximate value at point x- 0.7 of the interpolation polynomial obtained using the Newton -Back difference formulas using the values of (-l,4),(0,11), (1,16) (2,13) ? A) 12.067 B) 15.067 C) 14.067 D) 18.067 E) 10.067

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: 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: Are there any nonconstant polynomials in Z[x] that have multiplicativeinverses? Explain your answer

A: No, there is no any nonconstant polynomial in Z[x] that have multiplicative inverse.

Q: Use a linear approximation to estimate V26. Whot neint

A:

Q: 2. Use a lincar approximation to estimate /9.3.

A: In this question we have to use a linear approximation to estimate 9.3.

Q: Find the 3rd degree interpolating polynomial by Newton's backward formula X f(X) Af(X;) A²f(X;)…

A:

Q: Construct the Lagrange Interpolation polynomial for the fundlion y= Sinin taking the points. 6.

A: Given  y=sin(πx)x0=0,x1=1/6,x2=1/2

Q: Calculate approximations of tan(π/4-0.1) by using Taylor polynomials P₁(x), P2(x), P3(x). Use c=π/4.…

A: The given function is fx=tanπ4-0.1 To find: P1x, P2x, P3x about the center c=π4.

Q: Interpolate the value at 5th position from the f ta: dependent variable : 3 5 anctions : 170 ? 120…

A: Introduction: The formula for Lagrange's interpolation is given by,…

Q: From the given data, identify f(4) using Newton's polynomial. (2,10), (3,15), (5,25), (8,40)

A: Explanation of the solution is given below....

Q: When using yi=f(xi) for i=0,1, ..., n to find the Lagrange interpolating polynomial ---p(x), p(xi)…

A:

Q: The following table shows data of velocity versus time that has been collected by an engineer in a…

A: The Lagrange's polynomial that passes through the points x0, y0, x1, y1, x2, y2 can be estimated…

Q: Construct piece-wise linear polynomials for function f(x) = over the interval (0,0.4] with h= 0.2.…

A: Given  fx=11+x2 Interval: 0,  0.4 We first use piece-wise linear polynomials to interpolate the…

Q: i) what ins the nE Taylor polynomial , la) of a fune bien fx) at x-c? What does Taylor's Theorem say…

A: We have to find the Taylor's polynomial pn(x) of a function at x=c

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: 4. Compute f'dr by using fundamental theorem of integral calculus.

A:

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. Estimate the root of f(x) = In x; ɛEs = 0.1%. Start the computation with values of xl = xi-1 =…

A:

Q: Evaluate the improper intergal 1 dr using the residue theorem. (x² + 4)?

A: Solving imroper integral using residue theorem

Q: Find the 3rd degree interpolating polynomial by Newton's backward formula f(X;) Af(X,) A²f(X,)…

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: : Use Bisection method to solve f(x) = 668.06 -0.146843X (1 - e )- 40 with Xu = 16 %3D and X1 = 12…

A: The function is fx=668.06x1-e-0.146843x-40 with the bounds xu=16 and xl=12. The error is less than…

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: Use Newton’s method to find thezeros of ƒ(x) = 4x4 - 4x2 using the given starting values. x0 = 0.8…

A:

Q: Show that the Maclaurin polynomials for f (x) = ln(1 + x) are

A: The given function is fx=ln 1+x. fx=ln 1+x f0=0 f'x=11+x f'0=1 f''x=-11+x2 f''0=-1…

Q: . Use linear approximation to find v100.7

A: Linear Approximation For a function of any given value, the closest estimate of a function is to be…

Q: Show that ! fransform fix into It fn, linear "difference equation: equadion: SkH= +1. JKH

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: Compute for the z-score of x = 50, µ = 78.30, and o = 16. (Express your answer in two decimal…

A: We have to find z score for given data.

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

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: 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: T (F) H (btu/lb) 800 1000 1200 1400 1600 1303.6 1458.4 1585.3 1706.1 1826.1

A: We can solve this by using Lagrange's interpolating polynomials of degree 2

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

A:

Q: hat is the 5th Order Taylor Polynomial for f(x) = V1 + x where x = 0?

A:

Q: P"n+1 (x) – xP", (x) = (n+1)P,(x) = P,(x) %3D -

A:

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

A: According to the given information, Consider the given function.

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: Find the secod Lagrange înterpolation polynomial that rn tercepts f(x)= x+xe*+sinx at points…

A:

Q: section method to

A: Given,         f(x)=x-cos(x);     0, π

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

A:

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.