MCS 320 Quiz 7 Friday 14 October 2005

>

restart;

1. Show that

                 n

              ----               1

             >        k^3 = --- n^2 (n+1)^2

              ----              4

               k=1

ANSWER :

>	s := sum(k^3,k=1..n);

>	factor(s);

2. Give the Maple command to define the function defined by the integral of sin(x^2) for x from 0 to t.

   For any number t, the function should return a floating-point approximation (precision depending on Digits) for f(t).

   Give the Maple command to compute the derivative function f'.  What is f'(2)?

ANSWER :

>	f := t -> evalf(Int(sin(x^2),x=0..t));

>

f(2);

>	Df := D(f);

>

Df(2);