Gaussian Quadrature Using Gaussian quadrature with two points, approximate the integral: int_(-1)^1 (1)/(1+x^(2))dx Linear Regression The following data is given: x=[1,2,3,4,5],y=[2.2,2.8,3.6,4.5,5.1] Fit a linear regression model of the form y=a+bx. Determine the coefficients a and b using the least-squares method. 9. Lagrange Interpolating Polyn solutionspile.com

Question

Gaussian Quadrature Using Gaussian quadrature with two points, approximate the integral:

\int_(-1)^1 (1)/(1+x^(2))dx

Linear Regression The following data is given:

x=[1,2,3,4,5],y=[2.2,2.8,3.6,4.5,5.1]

Fit a linear regression model of the form

y=a+bx

. Determine the coefficients

a

and

b

using the least-squares method. 9. Lagrange Interpolating Polynomial Using the data:

x=[2,3,5],f(x)=[4,7,11]

construct the Lagrange interpolating polynomial of order 1. Evaluate

f(4)

. 10. Newton Divided Difference Using the data:

x=[1,2,3,4],f(x)=[1,8,27,64]

construct the Newton divided difference interpolation polynomial. Evaluate

f(2.5)

. 11. Weighted Mean Value Theorem for Integrals Verify the Weighted Mean Value Theorem for Integrals for the function

f(x)=e^(x)

over the interval

0,1

. Find the value of

c

that satisfies the theorem. 3

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