The following table presents the temperature in different minutes that were taken from'a cup of coffee. time(minutes) temperature (°C) 1 39 3 38.4 36.2 When constructing the interpolation polynomial of degree two, one has that the linear term is accompanied by the coefficient 0.5 -0.34 0.2 -0.4

Q: Find the interpolating polynomial of the following points or functions using Newton's

A: Given: The points -2, 2, -1, -2, 1, 3 and 3, -3. To find: Interpolating polynomial.

Q: Use this interpolating polynomial for the data points f(x) 1 0-368 1-2 0-301 1-3 0-273 1.5 0-223 To…

A:

Q: 7.) Explain why the eror term Rn(x) is ficitely bonded in every Tayler polynomial. Asnincreases, why…

A: Nothing

Q: In  the given question as follows , approximate the function at the given value of x, using the…

A: We have to approximate the function at the given value of x: fx=e4x,      f14 To find f14 we need to…

Q: Show that the Chebyshev polynomials have thefollowing properties: Tm(Tn(x)) = Tmn(x)

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Q: Consider the data (1, 10), (3,6). Then, Newton's polynomial that interpolates the data is

A: Given point is, Then,

Q: 8. Construct a natural cubic spline that interpolates the function f(x) = 1/(1+ x²) at x = -2, –…

A: Let the cubic spline polynomial of f(x) be H(x). Then Hx=fa+fa,ax-a+fa,a,bx-a2+fa,a,bx-a2x-b…

Q: 4. The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

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Q: 22/By using Newton's backward difference formula, construct an interpolating polynomial from the…

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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: A third degree polynomial passes through the points (0,9), (1.14), (2,17), (3,24), (4,41), (5,74)…

A: The value of X1=∆y3=y4-y3=24-17⇒X1=7and value of ∆2y2=X2=∆y3-∆y2=7-3=4⇒X2=4

Q: 67 Find the lowest order polynomial which approximates the function f(a)- (-x in the range 0 sxs1,…

A: We will use basic knowledge of numerical analysis to answer this question.

Q: 32. The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

A: Newton's farword diffrence formula

Q: A polynomial of degree n is developed using the interpolation method which based on the n-1 number…

A: Note : As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced…

A: In the question it is asked to construct interpolating polynomial using the table given in question.

Q: Determine the linear interpolating polynomial that passes through the points (2,4) and (5,1). p(x) =…

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Q: From the given data,identify f(4) using a Lagrance and Newton's polynomial…

A:

Q: In the table below, there are twelve rates over the period of time 2008 till 2019. You will choose a…

A: Regression equation are used to predict the variable based on the another. If the regression…

Q: Suppose xo. X1....., are distinct numbers in the interval [a,b] and f € C**[a,b). Then, for each x…

A: Suppose x0, x1, . . . xn are distinct numbers in the interval  and f∈Cn+1a, b. Then for each x in a,…

Q: (2) Construct the Simpson 3/8-th formula to approximate f(x)dr by using La- grange interpolating…

A: Given: ∫abf(x) dx and the function f(x), where the interval of integration a, b is divided into n=3…

Q: A researcher had collected data on the forces exerted on the wires in a prosthetic limb during a…

A:

Q: 2. Construct the interpolating polynomial of degree 4 using divided difference for the data given…

A: Given: x 0 1 2.5 3 4.5 5 6 y 2 5.4375 7.3516 7.5625 8.4453 9.1875 12 To find: Construct the…

Q: The following data of the velocity of a body is given as a function of time Time (s) 0. 15 18 22 24…

A:

Q: Two similar, but different ones. Consider the function f(x)=exp(x). Let p in P, be the interpolation…

A:

Q: Q1 Table below contains dataset of a robotic arm during a force measurement on a thigh phantom.…

A: given data  Time(s) 10.5 13.1 15.2 Force(N) 9.27 11.90 13.83 (A) lagrange interpolating…

Q: The following table lists monthly life insurance premiums for a $500,000 policy for females of…

A: The cubic polynomial regression equation can be computed using the technology. To find the equation,…

Q: b) The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in…

A:

Q: Determine the 3rd degree polynomial for the given set of data(x.y). 1. 1.3 2.4 3.7 3.8 5.1 y -6.3…

A:

Q: Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial…

A:

Q: The following table shows the lifting force on an aircraft wing measured in a wind tunnel at various…

A: let the polynomial of degree 5 be                                                  Lifting…

Q: * The Simpson's Rule gives the exact result when applied to any polynomial .of degree-➖➖➖➖➖➖➖or less…

A: Simpson's Rule: It is a numerical method for approximating the integral of a function between two…

Q: Define the Newton form of the interpolating polynomial?

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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: What is the order of the unique Lagrange inter- polating polynomial that passes through n + 1 data…

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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: How many local extrema can a polynomial P of degree n have?

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Q: In a well site, a directional drilling is planned. The reference points are given in the table…

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Q: A car traveling along a straight road is clocked at a number of points. The data from the…

A: Initially  Use a Hermite polynomial to predict the position of the car and its speed when t = 10 s.…

Q: A Cubic polynomial is dlefined by the table 3. 10 tind the equation of the palyinmal Using Lagrange…

A:

Q: Derive interpolating polynomial for log₁0 1=0, log₁, 2=0.3010, log, 3=0.4771, and hence calculate…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 2-Suppose that you have n data points (x1, y1), ..., (xn, yn), with the xi all distinct. Which of…

A: Question 2 is related to Existence and Uniqueness of interpolating polynomials Question 3 is asking…

Q: Consider the following data (xYk): (-2,0), (1,– 1), (3, -2). Find the interpolation polynomial P(x)…

A: Given x0=-2 , y0=0         x1=1 ,      y1=-1        x2=3 ,      y2=-2The interploting polynomial…

Q: The following table shows the lifting force on an aircraft wing measured in a wind tunnel at various…

A: Solution: The polynomial of five degree is P(x)=a0+a1x+a2x2+a3x3+a4x4+a5x5. Consider, a0=x1,a1=x2,…

Q: The following data gives the melting points of an alloy of lead and zinc. Percentage of lead in the…

A:

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: The following data represents the relationship between the drying time of a certain varnish and the…

A: Data represents the relationship between the drying time of a certain varnish and the amount of…