Targil 4

1. Question 1 - Plotting the Legendre polynomial
The Mathematica code I used to plot the Legendre polynomial P10(x) is the following:
code
And the received graph:
graph

2. Question 2 - Calculating the Legendre polynomials for x=0.66
The Mathematica code I used to calculate and plot the values of the Legendre polynomial and its derivative for x=.66 and n=1,2,3,....10 is the following:
code
code
And the received graph:
graph
Where the blue dots represent the Legendre polynomials values at x=0.66 and the orange dots represent their derivatives at the same point.

3. Question 3 - Calculating an integral
This integral can be easily calculated using Mathematica code:
Integrate[(1 + t)^0.5,{t,0,3}]
And the received answer is 4.66667.
We shall note that this integral can be also solved analytically which is always more accurate: code