<div class=""><pre>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)</pre></div>

Question

In: Physics

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)= 3^x-0.181and the values x₀₌-2, X₁=-1, X₂=0, X₃=1 and X₄=2.(Uses 4 decimal figures)

Expert Solution

genius_generous 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

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...

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...

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)

Q11: Use the Lagrange interpolating polynomial of degree three or less and four-digit chopping arithmetic to...

Q11: Use the Lagrange interpolating polynomial of degree three or less and four-digit chopping arithmetic to approximate cos 0.750 using the following values. Find an error bound for the approximation. cos 0.698 = 0.7661 ,cos 0.733 = 0.7432 cos 0.768 = 0.7193 cos 0.803 = 0.6946.

compute the 2-degree polynomial approximation of f(x)= 3x-e^x^2

Find the third MacLaurin polynomial for the function f(x) = e2x sin(3x)

Consider the polynomial f(x) = 3x 3 + 5x 2 − 58x − 40. Using MATLAB....

Consider the polynomial f(x) = 3x 3 + 5x 2 − 58x − 40. Using MATLAB. Find the three roots of the polynomial, i.e, x where f(x) = 0, using Newton’s method. Report the number of iterations taken by each algorithm using a tolerance of 10−8 .

consider f(x) = ln(x) use polynomial degree of 5!!! a) Approximate f(0.9) and f(1.1) b) Use...

consider f(x) = ln(x) use polynomial degree of 5!!! 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).

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and...

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve