MATH 1613 Length of Arc Spreadsheet Assignment

Name ______CPO ______

MATH 1613 Length of Arc Spreadsheet Assignment

Staple this sheet (as a cover page) to your printout.

Record the ark lengths determined by your spreadsheet for each of the given problems. Also record the value in the verification cell, G12.

Values for a b n Sum of Distances Actual Arc Length

2 4 10 ______

3 5 20 ______

1 6 20 ______

1 6 50 ______

2 5 80 ______

-3 2 50 ______

Elegance points:

Establish a validation for numeric data in cells c11 and c13. The value for b must be greater than a and the value for n must be positive. Print out a screen shot of this in action.

Create a graph (Excel calls it a chart) of the function showing the interval that is specified by the a and b values.

Composition of Functions Spreadsheet Assignment

Math 1303

1. Problem statement:

We seek a spreadsheet which will allow input the limits of an interval and the number of divisions of the interval and calculate the length of an arc for a function on that interval.

2. Instructions:

Begin the worksheet using a solution template that includes a title, a description, the parameters of the worksheet, and the computations.

Cell Address Label

A1 Title:

C1 Length of an Arc

G1 <your name>

A3 Description:

C3 This spreadsheet plots a function and calculates

C4 the length of the arc on an interval that you specify

C5 using the number of intervals that you specify

A8 Parameters:

C8 a = beginning of interval

F8 f(x) = .5x^2 – 3x + 5

C10 b = end of interval

C12 number of divisions

E17 Sum of Distances

E20 Arc Length using integral

Below is an example similar to what the spreadsheet will look like if you enter these labels correctly.

Now we must "name" three of the cells.

§  Place the cell cursor in c9 and click on the name box
arrow.

§  Specify that the name of this cell will be a

§  Place the cell cursor in C11 and name this cell b

§  Place the cell cursor in C13 and name this cell n

Now we can use these cell names in our formulas – they will be absolute references that will not automatically adjust as we copy formulas.

The spreadsheet now contains all but the numbers and formulas to compute the function compositions. Enter the formulas specified below in the indicated cells. For some of the more complicated formulas, you may wish to copy and paste them from this document.

Cell Address Formula

C9 1

C11 4

C13 10

A16 =a

A17 =A16+(b-a)/n

B16 =0.5*A16^2-3*A16+5

B17 =IF(A17<=b,0.5*A17^2-3*A17+5,0)

C17 =IF(A17<=b, SQRT((B17-B16)^2+(A17-A16)^2),0)

E18 =SUM(C17:C120)

E21 =LN(SQRT(b^2-6*b+10)+b-3)/2+(b-3)*SQRT(b^2-6*b+10)/2-
LN(SQRT(a^2-6*a+10)+a-3)/2-(a-3)*SQRT(a^2-6*a+10)/2

Now some of the formulas must be copied down the spreadsheet.

Select Cells A17 – C17 as shown (in this sample, the formulas below have already been copied)

Now when you move the mouse curser over the small black corner square of the selection, you can drag that corner down and copy the formulas. Drag them down to row 120. You should see the formulas adjust (except for the use of the a, b, and c).

Parameters / a = beginning of interval / f(x) = .5x^2-3x+5
1
b = end of interval /
4
number of divisions
10
1 / 2.5
1.3 / 1.945 / 0.630892225 / Sum of Distances
1.6 / 1.48 / 0.553376002 / 4.099667
1.9 / 1.105 / 0.480234318
2.2 / 0.82 / 0.413793427 / Value using the Integral
2.5 / 0.625 / 0.357805813 / 4.105679
2.8 / 0.52 / 0.317844302

Now you should experiment with the values for a, b, and n and note that larger values of n give more accurate sums, more closely agreeing with the value given by the integral.

Use the intervals and number of divisions specified on the cover sheet to determine the sums and the actual values that the sums should approximate. Record your results on the cover sheet. Staple the print out of your spreadsheet to the cover sheet for submission at the beginning of the assigned class.