1. Find the Legendre polynomial PL(x) for L = 3,4,5,6
where the polynomian is the series solution for Legendre
equation
2. Find the other solution QL(x) for the Legendre
equation for L = 0,1,2
Please explain in full.
Find the Taylor series or polynomial generated by the following
functions
a. )f(x) √ x centred at x=4 , of order 3
b.) f(x) cosh x= e^x+e^-x/(2), centred at x=0
c.) f(x) = x tan^-1x^2 , centred at x=0
d.) f(x) = 1/(√1+x^3) , centred at x=0 , of order 4
e.) f(x) = cos(2x+pie/2) centred at x= pie/4
Using laplace transformations, find the charge and current of an
LRC circuit in series where L=1/2h, R=10ohm, C=1/50f, E(t)=300V,
q(0)=0C, i(0)=0A. ( Lq'' + Rq' + (1/C)q = E(t) ).
The answer is q(t) = 10 - (10e^-3t)cos(3t) -
(10e^-3t)sin(3t) and i(t) =
(60e^-3t)sin(3t).
Using Laplace transform, find the load and current of the LRC
series circuit where L = 1 / 2h, R = 10ohms, C = 1 / 30f, E (t) =
300V, q (0) = 0C, i (0 ) = 0A
Let f(x) = 1 + x − x2 +ex-1.
(a) Find the second Taylor polynomial T2(x) for f(x)
based at b = 1.
b) Find (and justify) an error bound for |f(x) − T2(x)| on the
interval
[0.9, 1.1]. The f(x) - T2(x) is absolute value.
Please answer both questions cause it will be hard to post them
separately.
A particle is bound between x = -L to x = L where L = 0.1 nm.
The wave function is given by:
a) Find A
b) What is the probability of finding the particle between -0.05
nm and 0.05 nm?