Find the Lagrange and the Newton forms of the interpolating polynomial for these data: -2 0 1 f(x) 1 -1 Write both polynomials in the form a + bx + cx² to verify that they are identical as functions.

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: Given the function f(x). Suppose that the Newton's interpolating polynomial P() of f(x) at the…

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Q: 2. Given these data | 1 | 3 6 DA 19 | 7 f(x) 3 99 291 Estimate using Newton's interpolating…

A: Newton's divided difference interpolation formula is:…

Q: Find the Newton's polynomial which interpolating the following data. 1 2 3 4 5 f(x) 3.6 1.8 1.2 0.9…

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Q: Given a function ƒ (x). Suppose that, the Newton's interpolating polynomial P2(x) of f (x) at the…

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Q: (h) Write down the Lagrange's polynomial through (x0, fo), (x1, f1), (x2, f2). Hence express

A: h.  we have given the set of tabular values (x0,f0),(x1,f1),(x2,f2)we know that the lagrange's…

Q: A function f(x) is given as e-x * (x2+5x+2) + 1 = 0. Let a = 0 and b = -1. Find the root between a…

A: Bisection Method: Consider f(x)=0  For f(a)f(b)<0 Then root lies between a and b Then we choose…

Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(3) = 41 and the…

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Q: Q1. Find the Lagrange interpolation polynomial for the function y = f(x),and find the value of…

A: Introduction: Polynomial interpolation is the interpolation of a given records set via way of means…

Q: Given the following table find the value of y when x = 3 by interpolation using Newton's Divided…

A: Given x 2 4 5 7 y 15 140 290 750

Q: Given the data 2 5 6 f(x) 4 5.25 19.75 36 a) Calculate f (4) using Newton's interpolating…

A: (a) Here the given data is  We know the Newton's interpolating polynomial is…

Q: (a) Find the equation of the following curve Ax) using Newton's divided difference polynomial.…

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Q: Find the value of C such that the fnction Continubus on (-00,00) Cx +1 for XS 2 f(x)= r4x+I-3 for…

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Q: Use Newton-Raphson's Method to approximate the real solution of the following function. f(x) = 2sinx…

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Q: Find the newton polynomial formula for the given data 4 6. 10 f(x) 8 16

A: To give the Newton polynomial formula the given data.

Q: find the value of f(4) using the Lagrange's polynomial of at most degree3 from the data 3 7. y=f(x)…

A: If y=fx takes the values y0,y1,....,yn corresponding to x0,x1,....,xn then the Lagrange's…

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 6 P6(x) =

A: nth Maclaurin polynomial for the function :       Pn(x) =  ∑i=0n fi(0)i!xi = f(0)+f'(0)x + f''(0)…

Q: find the zero and its order for the FAO function fl2)=1- 1i+ 2+ e? .

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Q: Find the nth Maclaurin polynomial for the function. 2x 3 f(x) n = 4 x + 1 Pa(x) =

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Q: Find the roots of the polynomial: f (x) = a – a? +.1

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Q: Find the roots using Bairstow's method of the function f (x) = x* – 2x3 + 2x² + 3x – 4. Use u, = 1…

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Q: Using Newton's Divided Difference, the polynomial that interpolates ex at the points Xo=0, xı=1, and…

A: For the solution follow the next step.

Q: Given a function f (x). Suppose that, the Newton's interpolating polynomial P2(x) of f (x) at the…

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Q: Find the nth Maclaurin polynomial for the function f(x) = sin x, n = 5

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: When calculating the first Lagrange polynomial using x0, X1 we obtain L,(x) =x-3, then Xo and x, are…

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Q: Find the values of the coefficients a, b and c so that the conditions f(0) = -1, f'(0) = -3, and f"…

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Q: Use Newton's interpolating polynomial to determine y at x = 4 to the best possible accuracy x 3 5.25…

A: Given: x 3 5 2 6 1 y=fx 5.25 19.55 4 36 4.65 To find: y at x=4 using Newton's interpolating…

Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(3) = 41 and the…

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Q: Given the function g(t) = – 10(t – 5)°(t + 3)°(t – 6), its roots are and their multipicities are

A: To determine the roots of the function and their multiplicities.

Q: Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(5) = 147 and the…

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Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 6

A: A Maclaurin series is the expansion of the Taylor series of a function about zero.

Q: Ex1: Find the first seven root of the polynomial equation f (x) = 2x - 9x² + 12x – 6 using (a)…

A: Differentiate the function fx=2x3-9x2+12x-6 with respect to x, to find f'(x). Substitute 0 for x0 in…

Q: Determine the approximate value of one of the roots of the function f(x) = x3 – x + 1 by applying…

A: Given  The function is f(x) = x3-x+1 .

Q: Find the nth Maclaurin polynomial for the function. f(x) = sec(x), n = 2 P2(x) = %3D

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Q: (e) Write McLaurin polynomial of 3rd degree for the function f(x)= V1-

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Q: Using Newton's Divided Difference, the polynomial that interpolates ex at the points Xo=0, x1 = 1,…

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Q: By using Lagrange's interpolation polynomial of order 1 through 3. Calculate f(3.5) from the…

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Q: Given the following table of values, use Lagrange Interpolation to find the 2nd degree polynomial of…

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Q: Determine the approximate value of one of the roots of the function f(x) = –2x³ + 3x – 5 by applying…

A: The given function is fx=-2x3+3x-5. Observe that, f-1=-2-13+3-1-5=2-3-5=-6 Similarly,…

Q: for the function f (x) = x + . Estimate a) Lagrange interpolating polynomial b) Newton's…

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Q: 1. Find the Lagrange form of the interpolating polynomial for the following table of values: *| 1/3…

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Q: Let f(x) = x3+5x+3. Construct the divided-difference table based = 2, a2 3, a3 - 4, x4 5, axs 6, and…

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Q: Assume that f(x)=Dx2). Find Newton Polynomial P1 (x) for the points xo = 4.0 and x1 = 9.0. %3D %3D…

A: We have to solve given problem:

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: For the function f(x) = x² +3x + 1 (a) Construct the divided difference table for the points xo=1,…

A: Introduction: For the given set of data points x0,y0,x1,y1,...,xn,yn, the divide difference table is…

Q: For the following values determine Newtons polynomial and approximate x-1 -0.4 0.4 0.8 1.2 T()…

A: To determine Newton’s polynomial and approximate

Q: Find the roots of the following using the indicated method|f (x)| < 0.0001 1. f (æ) = 3x³ + 2x² + 1…

A: Note: It is assumed that B.M. is the abbreviation for "Bisection Method."   The bisection method…

Q: Use the 3rd Degree Maclaurin polynomial for g(x) = x COS to approximate the value of 0.2 cos(0.1).…

A: We have to find 3rd degree polynomial for the given function.

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 5 P5(x) =

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Q: 2. Given these data X 1 3 7 f(x) 3 19 99 291 Estimate using Newton's interpolating polynomial and…

A: x fx fxi, xi+1 fxi, xi+1,xi+2 fxi, xi+1,xi+2, xi+3 fxi, xi+1,xi+2, xi+3, xi+4 1 3             3…

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.