find Lagrange polynomials that approximate f(x)=x^3, a) find the linear interpolation p1(x) using the nodes X0=-1...

find Lagrange polynomials that approximate f(x)=x^3,

a) find the linear interpolation p1(x) using the nodes X0=-1 and X1=0

b) find the quadratic interpolation polynomial p2(x) using the nodes x0=-1,x1=0, x2=1

c) find the cubic interpolation polynomials p3(x) using the nodes x0=-1, x1=0 , x2=1 and x3=2.

d) find the linear interpolation polynomial p1(x) using the nodes x0=1 and x1=2

e) find the quadratic interpolation polynomial p2(x) using the nodes x0=0 ,x1=1 and x2=2

Expert Solution

Colby Messinger answered 2 years ago

Find the lagrange polynomials that approximate f(x) = x3 a ) Find the linear interpolation polynomial...

Find the lagrange polynomials that approximate f(x) = x3 a ) Find the linear interpolation polynomial P1(x) using the nodes x0= -1 and x1 = 0 b) Find the quadratic interpolation polynomial P2(x) using the nodes x0= -1 and x1 = 0 and x2 = 1 c) Find the cubic interpolation polynomial P3(x) using the nodes x0= -1 and x1 = 0 and x2 = 1 and x3=2 d) Find the linear interpolation polynomial P1(x) using the nodes x0= 1...

Let f(x) = x + 2/x a) Use quadratic Lagrange interpolation based on the nodes x0=1,...

Let f(x) = x + 2/x a) Use quadratic Lagrange interpolation based on the nodes x0=1, x1=2, and x2=2.5 to approximate f(1.5) and f(1.2) b) Use cubic Lagrange interpolation based on the nodes x0=0.5, x1=1, and x2=2 to approximate f(1.5) and f(1.2)

Use the Lagrange interpolating polynomial to approximate √3 with the function f(x)= 3x-0.181and the values x0=-2,...

Use the Lagrange interpolating polynomial to approximate √3 with the function f(x)= 3x-0.181and the values x0=-2, X1=-1, X2=0, X3=1 and X4=2.(Uses 4 decimal figures)

Use Lagrange interpolation to find the polynomial p3(x) of degree 3 or less, that agree with...

Use Lagrange interpolation to find the polynomial p3(x) of degree 3 or less, that agree with the following data: p3(−1) = 3, p3(0) = −4, p3(1) = 5, and p3(2) = −6. Using python to solve

Find f(x) if f is a linear function that has given properties. f(-1)=1, f(3)=9 f(x)=

Using the Composite Trapezoidal Rule, with evenly spaced nodes, and n=3, find an approximate value for...

Using the Composite Trapezoidal Rule, with evenly spaced nodes, and n=3, find an approximate value for interval where b=1 and a=0, e^(-x^2)dx. Estimate the error.

Factor Values Find the numerical value of the following factors using (a) linear interpolation (b) the...

Factor Values Find the numerical value of the following factors using (a) linear interpolation (b) the appropriate formula 1. (F/P,18%,33) 2. (A/G,12%,54)

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative...

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative and linear approximation, estimate f(9.1).

consider f(x) = ln(x) a) Approximate f(0.9) and f(1.1) b) Use Taylor remainder to find an...

consider f(x) = ln(x) a) Approximate f(0.9) and f(1.1) b) Use Taylor remainder to find an error formula for Taylor polynomial. Give error bounds for each of the two approximations in (a). Which of the two approximations in part (a) is closer to correct value? c) Compare an actual error in each case with error bound in part (b).

consider f(x) = ln(x) a) Approximate f(0.9) and f(1.1) b) Use Taylor remainder to find an...

consider f(x) = ln(x) a) Approximate f(0.9) and f(1.1) b) Use Taylor remainder to find an error formula for Taylor polynomial. Give error bounds for each of the two approximations in (a). Which of the two approximations in part (a) is closer to correct value? c) Compare an actual error in each case with error bound in part (b).

Question

find Lagrange polynomials that approximate f(x)=x^3, a) find the linear interpolation p1(x) using the nodes X0=-1...

Solutions

Expert Solution

Related Solutions

Find the lagrange polynomials that approximate f(x) = x3 a ) Find the linear interpolation polynomial...

Let f(x) = x + 2/x a) Use quadratic Lagrange interpolation based on the nodes x0=1,...

Use the Lagrange interpolating polynomial to approximate √3 with the function f(x)= 3x-0.181and the values x0=-2,...

Use Lagrange interpolation to find the polynomial p3(x) of degree 3 or less, that agree with...

Find f(x) if f is a linear function that has given properties. f(-1)=1, f(3)=9 f(x)=

Using the Composite Trapezoidal Rule, with evenly spaced nodes, and n=3, find an approximate value for...

Factor Values Find the numerical value of the following factors using (a) linear interpolation (b) the...

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative...

consider f(x) = ln(x) a) Approximate f(0.9) and f(1.1) b) Use Taylor remainder to find an...

consider f(x) = ln(x) a) Approximate f(0.9) and f(1.1) b) Use Taylor remainder to find an...