(Solved): Lagrange Interpolating Polynomial Using the data: x=[2,3,5],f(x)=[4,7,11], construct the Lagrange in ...
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
cthat satisfies the theorem. 3 12. Taylor Series Approximate
e^(x)at
x=0.5using a Taylor series expansion about
x=0up to the third-order term. Compare the approximation to the actual value of
e^(0.5). 13. Curve Fitting (Least Squares Error) Fit a quadratic polynomial of the form
y=a+bx+cx^(2)to the following data:
x=[1,2,3,4],y=[1,1.5,2.2,3.1].Determine the coefficients
a,b,cusing the least-squares method. 14. Multiple Linear Regression Given the following data:
x_(1)=[1,2,3,4],x_(2)=[2,4,6,8],y=[2.5,3.6,5.1,6.3],fit a multiple linear regression model of the form
y=a+b_(1)x_(1)+b_(2)x_(2). Find the coefficients
a,b_(1),b_(2). 15. Curve Fitting Interpolation Given the data:
x=[1,3,5],y=[2,4,6]construct a quadratic interpolation polynomial. Evaluate
y(4).
