Write down the Lagrange form of the interpolating polynomial P(x) that satisfies P(x) = f(x) for x = = 1,...,n and x1 < x2 < · · · < xn• (1) Find the form of the polynomial that interpolates f(x) = 1 through the points x = x1 = 0.5, x2 = 1 and x3 = 3, then simplify it. Use this polynomial to estimate the value of ƒ (2) and find the error from the actual value.

Q: Let f(x) = x + √2x3 + x. Verify whether f[0, 1, 2, 3, 4] = f [0, 1, л, е, -1].

A: The details solution of the given question is given below in step 2.

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…

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Q: Let k(x) = 1 -x4, where j(x) = y + k(x) and y = x6 - x2. Describe the graph of j(x) based on the…

A: Given: k(x)=1-x4 where, j(x)=y+ k(x) y=x6-x2 Then j(x)=x6-x2+1-x4j(x)=x6-x4-x2+1 The zeroes of the…

Q: f(x) = 8+x 8 - x on [4, 6].

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Q: Find the maximum point for the function f(x) = 1 + 12x – 4x O (-1, -7) O (2, -7) O (0, 1) (1, 9)

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Q: 1 >Use the following models to consider the function f(x)=; on the interval 1+x? [-5,5]. (1)…

A: The function given is as follows: fx=11+x2 (1) We are asked to find the interpolating polynomial of…

Q: Find a polynomial y = p(x) of degree 4 that goes through the points (0, 4), (1, 2), (2, -4), (3,…

A: solution of the given question is like this:

Q: Show that the product rule works for the case f (x) = x2, g (x) = x3.

A: Given that, fx=x2gx=x3 We have to show that the product rule works for the case of given functions.

Q: Compute the difference quotient (a) f(x) = -3+7x (b) f(x) = 5x²5x+2 Submit Question f(x + h) − f(x),…

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Q: Find the zeros of the polynomials f (x)=x'-5x² – 2x + 24, If it is given that the product of its two…

A: *to find:- roots of the given equation.

Q: Let f ( x ) = x^ 2 − 1 and g ( x ) = 3 x. Find ( f ∘ g ) ( x ). group of answers 3x^3 − 3x 3 x^2…

A: Given functions, f(x)=x2-1 and  g(x)=3x

Q: Let f and g be define f(x) = x-5 and g(x)=x²-1. Express the following functions as the sum,…

A: As per Bartleby rules we have to answer only first three questions.