2-6-10.html

Spreadsheet in Maple

2-6 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;

> f(3);

> f(24);

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2-7 How is the number pattern related to the successive derivatives of tan(x) formed?

> diff(tan(x),x);

2-8 How is the number pattern related to the successive derivatives of cot(x) formed?

> diff(cot(x),x);

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2-9 Express tan(nx) as a rational function of tan(x) for n = 0,1, 2,3,4,5,6

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

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

(4*tan(x)-4*tan(x)^3)/(1-6*tan(x)^2+tan(x)^4)

(5*tan(x)-10*tan(x)^3+tan(x)^5)/(1-10*tan(x)^2+5*ta...

(6*tan(x)-20*tan(x)^3+6*tan(x)^5)/(1-15*tan(x)^2+15...

2-10 Study the number pattern associated with the indefinite integral of the function

> int(x^n*exp(x),x);

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