ex2-1.html

Spreadsheet in Maple

Use the spreadsheet in Maple to experiment with the 3x + 1 problem.

> f:=x->if x mod 2 =0 then x/2 else 3*x+1 fi:

How is the number pattern related to the sucessive derivatives of tan(x) formed?

> restart;

>

How is the number pattern related to the sucessive derivatives of cot(x) formed?

>

Express tan(nx) as a rational function of tan(x) for n = 1,2,3,4,5,6.

-2*tan(x)/(-1+tan(x)^2)

tan(x)*(-3+tan(x)^2)/(-1+3*tan(x)^2)

-4*tan(x)*(-1+tan(x)^2)/(1-6*tan(x)^2+tan(x)^4)

tan(x)*(5-10*tan(x)^2+tan(x)^4)/(1-10*tan(x)^2+5*ta...

Study the number pattern associated with the indefinite integral of the function

.

List the Chebyshev polynomials Tn(x) for n = 0,1,2,3,4,5,6.