MATHS 159 Lab 4, Fall 2009

This lab is due on Friday, September 25, 2009.  Using MS Excel 2007 to create appropriate charts or graphs, answer each of the questions below.  Keep your Excel work for this assignment in one spreadsheet with multiple, clearly labeled worksheets.  Save this Excel file as LastnameFirstname15900XLab4.xlsx (i.e. MS Excel 2007 format), where 00X is chosen to be 001 or 002, as appropriate to the section in which you are enrolled. This Excel file is to be turned in along with your answers to the questions below.  Put all answers that require a written response, chart, or table into a single MS Word 2007 file.  Copy and paste your Excel tables and charts into the Word document with your written answers and save it as LastnameFirstname15900XLab4.docx (i.e. MS Word 2007 format).  Whenever possible, to save time and do less hand calculation, use Excel’s features to help with these questions. Be as neat and complete as possible.  Both your MS Word and Excel files should be emailed to our class Graduate Assistant, Priyanka Bhatlapenumarthi at bhrrpriyanka@gmail.com.

For this lab only:  You do not have to copy your Excel tables into the MS Word file.  Just create a separate worksheet for each problem/sub-problem your ONE Excel file.  In your Word file you will type your answers.  Feel free to refer to the Excel file without copying it into your Word file.

1. (A piecewise-defined function) Use the IF function to define the function f(x) as follows:  f(x) = -x² if x < 0; f(x) = x+1 if 0 ≤ x < 2; x² + 1 if x ≥ 2.  Make an Excel table of function values with the inputs -3, -2, -1, 0, 1, 2, 3, 4.  Then plot this function using Excel (the graphs should look like a graph of a function defined at all x-values in [-3, 4].  Note:  You may have to include more input values to get the graph to look “right”. 

2. (Grade book Revisited)  Create the grade book from Example 1 of Lecture 1.  Make sure average, total points, and percent are computed automatically by Excel.  Add in the following extra features:  Automatically compute a grade based on our class grading scale.  Also, highlight in red any cell for which the score is less than half of the total points possible.  Highlight in green any perfect score.  Highlight in yellow all grades of B or higher.  (Use conditional formatting to accomplish these color highlighting schemes.) 

MATHS 159 Fall 2009 Grades	Exam 1	Exam 2	Exam 3	Homework	Participation	Final Project	Total Points	Percent	Grade
Name/Points Possible	50	50	50	250	100	100	600	1	A
Aristotle, R.	30	34	25	151	45	80	365	61%	D-
Einstein, A.	35	19	43	246	70	99	512	85%	B
Galois, E.	34	27	38	247	34	95	475	79%	C+
Gauss, K.	45	50	38	172	87	66	458	76%	C
Noether, E.	48	43	44	225	64	96	520	87%	B+
AVERAGE	38	35	38	208	60	87	466	78%	C+

3. (Plotting the Tangent Function) Find a way for Excel to produce a “better looking” graph of the tangent function than what we saw in Lecture 5, Example 2.  Plot this graph!

4. (A Function and its Inverse) Use Excel to plot cosine and inverse cosine functions on the same graph – make sure to clearly identify each function.  In your MS Word file, include a printed copy of your graph.

5. (Volume of Water in a Tank)  Use Excel to reproduce the spreadsheet for Lecture 5, Example 6 with the extra property that if the a – values in column A are changed from 10 to another value, such as 20, the h – values won’t change and everything else in the spreadsheet will automatically change accordingly.

a. Use this spreadsheet to estimate how much water is left in the tank at times t = 0, 10, 20, 30, 40, 50, and 60 minutes.

b. Use this spreadsheet to estimate the instantaneous flow rate at times t = 0, 10, 20, 30, 40, 50, and 60 minutes. 

c. At what time is the tank draining the most rapidly?

6. (The Derivative and Tangent Lines) This problem is based on an example and lab problem from Shannon Schumann at the University of Colorado at Colorado Springs Mathematics Department.  Look at the following Excel Worksheet Tangent Line Example to illustrate the derivative with tangent lines.  Reproduce this worksheet with its built-in interactivity, but use the function f(x) = sin x on the interval [0, 2p], set a = p, and cut the interval into 20 equal pieces, instead of 10 equal pieces.  Changing entries in the blue cells should cause the entire spreadsheet to automatically change accordingly!  Put your name in the graph instead of “Michael Karls”.