Exercises

1. Calculate the first and second derivative of wrt .
2. Given the polynomial find the roots and any local minima and maxima of . Check your solutions with a plot of the polynomial.
3. Given calculate the integral of and with respect to . Check that Maples answers are correct by differentiating the results.
4. Compute the following integrals

   

5. Compute the following sums
6. Compute a formula for the sum of the first integers and also the sum of the squares of the first integers. I.e. compute and simplify the sums
7. Given the function , define the function in Maple and compute the value of the function at and then graph the function in the region [,].
8. Input the following Matrix into Maple

   

   1. Compute the characteristic polynomial of . Hint: use the charmat and det commands in the linear algebra package linalg.
   2. Compute the eigenvalues of . Hint: use the solve or factor commands to find the roots of the characteristic polynomial.
9. Use the solve command to solve the linear system