Q2. (a) Compare and contrast the following four interpolated polynomials. Lagrange Polynomial. (i) (ii) Newton Divided-Difference Polynomial. (iii) Hermite Polynomial. (iv) Cubic Spline Polynomial.

Q: ving polynomials for x = 2 and x = -2, ree of each polynomial. %3D %D -10 + 3

A: The degree of a polynomial is the highest power of the variable in a polynomial expression.

Q: Consider the data in Table. Using direct fit polynomials, calculate P₂(4.25) using: (a) the first…

A: Given: A data in the table. x F(x) 3 3.3333 3.5 3.7857 4 4.2500 4.5 4.5222 5 5.2000…

Q: Consider the polynomial P(x) = x² + 3x³ - 2x² − 3x +2. (a) Determine another polynomial Q equivalent…

A: P(x)= x4 + 3x3 -2x2 - 3x +2 a)  by using Horner's method Q(x)= 2 + x(-3+x(-2+x(3+x)))   {I am…

Q: 5. (a) Evaluate the polynomial y=2²-82² +12z-0.45 at z 2.378. Use 4-digit arithmetic with chopping.…

A: Given,y=x3-8x2+12x-0.45 and y=x-8x+12x-0.45To find: Value of given polynomials with chopping and…

Q: 2. Given the points (1,0.7),(2,0.73),(3,0.8),(4,0.75),(5,0.6). Use Lagrange polynomials to find the…

A: Given points are xi 1 2 3 4 5 yi 0.7 0.73 0.8 0.75 0.6 Here, i=0, 1, 2, 3, 4.

Q: Using pencil, paper and calculator, form the Lagrange interpolating polynomial corresponding to the…

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Q: 9. For the polynomial f(x) = x(3x + 1)(x – 2)², determine the leading coefficient, leading term,…

A: Given: fx=x3x+1x-22 Now solve the parenthesis we get, ⇒fx=3x4-11x3+8x2+4x                    ...(1)…

Q: Convert the following polynomials to factorial poly 1. (x-7)(x-6)(x - 5)(x+4) 2. (x+6) (x + 7)(x +…

A: We have to solve 1. (x-7)(x-6)(x-5)(x+4)2. (x+6)(x+7)(x+8)(x+9)(x-10)

Q: What are the zeros of the polynomial function ?(?) =(? + 5)(? − 3) A. {−5, −3} B. {5, −3} C. {−5,…

A: To find the zeros of the polynomial function.

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: Ans 1: (d) Degree of polynomial is 6Ans 2 : (b) Function changes its sign at x =…

Q: 10. Which of the following could describe the polynomial related to the graph? 6 -5 -4 -3 Þ -i 5 6…

A: According to the guidelines in case of multiple questions we are only allowed to do one question (…

Q: Find the equation of the curve that passes through the following points using the negative Factorial…

A: In the above ques- We have to find y at x = 8 Y (8) = ? We can easily see from table that x = 8 will…

Q: 4. which polynomial is accurate x = [2; 2.75; 4]; y = [0.5; 1/2.75; 0.25]] 0.0455 x² 0.1039x² -…

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Q: The value of a person's house (in thousands of dollars) from the years 2010 to 2021 can be modeled…

A: Given polynomial function is Vt=0.121t3-1.321t2+11.342t+206.283 We need to sketch the graph of the…

Q: 15. For the polynomial 3 x*-2x²+5x-8,state the following: a. The degree of the polynomial b. The…

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Q: 5. Find the best fit by a first degree polynomial for the following data: x -3 -1 0 2 y 8 5 4 1

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Q: Find f(x) and g(x) such that h(x) = (f o g)(x) and g(x)= 8-5x. h(x) = (8-5x) - 5(8-5x)2 +4(8-5x)-1…

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Q: Divide both polynomials by x – 4. 5. f(x) = x³ – 6x² + 5x + 12

A: We have to divide the polynomial by (x-4)

Q: Calculate the first three Legendre coefficients for f (x) = x² + 1 and then express the f(x) in…

A: The solution of the differential equations are the functions that satisfies the differential…

Q: Fit a cubic polynomial to the following data: X y 3 1.6 4 3.6 5 4.4 Determine the coefficients, r²…

A: Given data: let us start using cubic polynomial    X Y 3 1.6 4 3.6 5 4.4 7 3.4 8 2.2…

Q: II. Find an equation for the 7. 5th degree

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

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Q: 16. La(z) = -7 + 57z - 134z + 78 is the degree (at most) 3 interpolating polynomial for the dala in…

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Q: If In(9) = 2.1972 and In(10)=2.3025, using Langrange polynomial, find In(9.6) and the error.

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Q: 5. (a) Evaluate the polynomial y = x³ - 8x² + 12x −0.45 at a = 2.378. Use 4-digit arithmetic with…

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Q: Q// Fit a second-order polynomial to the following data: Y 9 8 3 7 9 11 9 6 1 7 1 3 10 9. 1 a. y =…

A: Given x y 9 8 0 3 7 9 11 9 6 1 0 0 0 7 1 3 8 10 9 1

Q: Consider the polynomial defined by p(x) = (x − a)(x − b) ... (x − z). a. How many additions and…

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Q: Give the degree and leading coefficient of the following polynomial function. f (x) = x³ (3 – 7x² –…

A: Here in the given polynomial, we have to find the degree and order of the polynomial.   The highest…

Q: 2. Using the given pairs of x and f(x), construct a an appropriate table (difference or divided…

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