Description

1. The rst 4 Legendre polynomials are given by:
.
Divide the display in 4 parts and plot in each part the Legendre polynomial li; i = 1;:::;4. (Use the subplot command).
2. a) Chebyshev polynomials of the rst kind are de ned by
Tn(t) = cos(narccost); t 2 [ 1;1]:
Plot, in the same gure, the polynomials T1;T2;T3:
b) Plot, in the same gure, the rst n Chebyshev polynomials of the rst kind, using the following reccurence formula:
Tn+1(x) = 2xTn(x) Tn 1(x); x 2 [ 1;1]; with T0(x) = 1 and T1(x) = x:
3. Taylor polynomial of -th degree, associated to the function f and the point x0; is given by . Plot, in the same
gure, the rst six Taylor polynomials for f(x) = ex and x0 = 0; on the interval [ 1;3]:

4. Considering h = 0:25; a = 1; ai = a + ih; i = 0;6; and f(x) = p5x2 + 1; construct the nite di⁄erences table.
5. For x0 = 2; x1 = 4; x2 = 6; x3 = 8 and f0 = 4; f1 = 8; f2 = 14; f3 = 16 construct the divided di⁄erences table.
1