Spring 2010

# assignments

due Fri Feb 5

## assignment 1

Evaluate the following integrals:
1. x⋅ln(xdx ;
2. t⋅sin(2tdt ;
3. p5⋅ln(pdp ;
4. x⋅5x dx ;
5.  π ∫ t⋅sin(3t) dt 0
;
6. First make a substitution and then use integration by parts to evaluate the integral.
1. ;
2. x5ex2 dx  .
due Fri Feb 19

## assignment 2

Exercises from the course text, i.e. Stewart's Single Variable Calculus, Volume 2. Section 8.4: Integration of Rational Functions by Partial Fractions.
• Exercise 8.4: 10, 12, 14, 22, 26, 28, 50 and 52.
• Challenge questions (optional but will improve marks)
• Exercise 8.4: 48, 50, 57 and 65.
due Mon Mar 8

## assignment 3

Reread the section on partial fractions!
Exercises:-
• Section 8.4 (Partial fractions): 2, 4, 6 (read question carefully).
• Section 6.2 (Volumes): 52. 68, 71.
• Section 6.3 (Cylindrical shells): 18, 20, 30.

due Mon Apr 12

## assignment 4

Laboratory Project: Running Circles Around Circles. (At the end of Section 11.1 on Parametric Equations.)
This project is closely related to the toy Spirograph.

Please use the following Mathematica notebook, located here, as a basis for your work. Note that the notebook has to be saved onto your own login area and then opened with Mathematica afterwards. Furthermore, make sure the file is saved as .nb as the file type not .txt .
You can also use the SAGE notebook, located here. Please save this file and then use SAGE to start an untitled worksheet, and then you upload the file to the worksheet.
due Wed Apr 28

## assignment 5

Exercises; Section 12.1 (Sequences):-
• Ex: 20, 22, 24, 26, 40, 44, 62, 81.
• Optional:
• Laboratory Project: Logistic Sequences: Q1 to Q4. Can only plot about 40 terms for last question with following Mathematica notebook. Download the Mathematica notebook (Iterates of the Logistic Map in 3D) for this project here.
due Mon May 3

## End of term exam

due Mon May 10 1:00 pm

## Final exam

http://cs.marlboro.edu/ courses/ spring2010/calc2/ special/assignments