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)

Expert Solution

Colby Messinger answered 2 years ago

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

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)

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...

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

Let f(x) = sin(πx). • x0 = 1,x1 = 1.25, and x2 = 1.6 are given....

Let f(x) = sin(πx). • x0 = 1,x1 = 1.25, and x2 = 1.6 are given. Construct Newton’s DividedDiﬀerence polynomial of degree at most two. • x0 = 1,x1 = 1.25,x2 = 1.6 and x3 = 2 are given. Construct Newton’s Divided-Diﬀerence polynomial of degree at most three.

For the given function f(x) = cos(x), let x0 = 0, x1 = 0.25, and x2...

For the given function f(x) = cos(x), let x0 = 0, x1 = 0.25, and x2 = 0.5. Construct interpolation polynomials of degree at most one and at most two to approximate f(0.15)

Use the method of Lagrange multipliers to find the extreme values of f(x, y) = 2x^2−3y^2...

Use the method of Lagrange multipliers to find the extreme values of f(x, y) = 2x^2−3y^2 subject to the constraint that x^2+y^2 = 3.

2. Let f(x) ≥ 0 on [1, 2] and suppose that f is integrable on [1,...

2. Let f(x) ≥ 0 on [1, 2] and suppose that f is integrable on [1, 2] with R 2 1 f(x)dx = 2 3 . Prove that f(x 2 ) is integrable on [1, √ 2] and √ 2 6 ≤ Z √ 2 1 f(x 2 )dx ≤ 1 3 .

Use Lagrange Multipliers to find any max or min values of f(x,y) = y^2 - 7x^2...

Use Lagrange Multipliers to find any max or min values of f(x,y) = y^2 - 7x^2 with the constraint x^2 + 2y^2 = 4

Consider polynomial interpolation of the function f(x)=1/(1+25x^2) on the interval [-1,1] by (1) an interpolating polynomial...

Consider polynomial interpolation of the function f(x)=1/(1+25x^2) on the interval [-1,1] by (1) an interpolating polynomial determined by m equidistant interpolation points, (2) an interpolating polynomial determined by interpolation at the m zeros of the Chebyshev polynomial T_m(x), and (3) by interpolating by cubic splines instead of by a polynomial. Estimate the approximation error by evaluation max_i |f(z_i)-p(z_i)| for many points z_i on [-1,1]. For instance, you could use 10m points z_i. The cubic spline interpolant can be determined in...

Question