The two home screens below show how the TI-92 can be used to estimate the length of a curve
y = f(x) for a <= x <= b
using the method described in the browser window. It uses the curve
y = sqrt(1 - x^2) for 0 <= x <= 1 using n = 10
as an example.
IMPORTANT: To evaluate the sum in the second screen press green-diamond ENTER rather than just ENTER. Pressing green-diamond ENTER uses approximate arithmetic rather than exact symbolic computation. Approximate arithmetic is faster and gives us the numeric estimate that we want.
Before looking at the questions about tennis raised in the browser window you may want to look at the help files for Tables of Values for Sequences
Don't forget to set the Graph MODE to SEQUENCE in order to produce a table of values for one or more sequences.
The home screen below shows how we start looking at questions about tennis.
The two screens below show how the Y= screen should be set up to produce a table of values for the sequences involved in the tennis questions. Notice the first of these two screens shows how the initial values of the sequences are entered using the constants youmake and oppmake to make it easier to answer other questions about tennis games with different strategies. Notice in the second screen that when the ENTER key is pressed the TI-92 computes the numeric initial values. The sequence u1 keeps track of your losses and the sequence u2 keeps track of your wins.
The screen below shows the table computed by the TI-92.
Now use the ideas illustrated above to answer questions about tennis.