- Evaluate to 30 decimal places.
- Input the following as a Maple function:
*f*(*x*) = .- a)
- Write this in a simpler form (that is, factor and reduce it).
- b)
- Draw the graph of the function for
*x*between 0 and 1). Adjust the vertical range so that some detail can be seen. - c)
- Compute the area of the part of the curve that lies above the
*x*-axis and between*x*= 0 and*x*= 5 (that is, integrate the function over the appropriate range of*x*values). Give your answer both in actual form and as a decimal approximation to about 10 places. - d)
- What is the value of the integral if you remove the factor of from the numerator?
- e)
- Use the derivative of
*f*(*x*) to determine for what real value*x*the function has a local maximum. Use an approximation to about 8 decimal places.

- Use the commands
`seq`

and`ithprime`

to generate a list of the first 20 primes. Compute the sum of these 20 primes, and give its integer factors. - Find the solutions of the system of equations
{
*x*^{2}-*y*^{2}= 4,*x*- 2*y*= 2}. - Draw a graph showing both cos
*x*and its fifth Taylor polynomial (that is, 1 -*x*^{2}+*x*^{4}) for*x*between -4 and 4. How many terms do you seem to need to get*good agreement*in this range.**Hint**: use a variation of the command`convert(taylor(cos(x),x,5),polynom)`

to make this work.Think of a suitable way to demonstrate that the approximation you have taken is

*good*.

2002-08-29