~SOME CALCULATOR PROCEDURES FOR THE TI-83~

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FINDING FUNCTIONAL VALUES

Table Method: Mode: Rad & function
Enter equation: Y1=
Press 2nd window to set up your table (Table Set)
(move to auto for integer values of x)
(move to ask for any value of x you want) (keep this setting)
(keep y at auto)
press 2nd Graph
enter desired x-value
y-value appears in 2nd column
Note:  For graphing purposes, Zoom Fit (menu 0), will graph the
           equation.  However, if a more complete graph is desired,
           change the x & y ranges in the window.  It's best to experiment
           with various ranges to see the effect on the graph. Looking at
           the range of values from your table will give you a good indication
           how to set up values in your window for a real good graph.

Using the trace button
When the graph is visible, clicking the trace button will place a symbol on the graph. Moving the cursor in different directions along the curve will give the coordinates of its location at the bottom of the screen. Error messages will occur is the y values are too large (overflow error) or if the x value entered is not in the range of the x values of the window. You make have to adjust the window ranges to get them. This is a very convenient way of finding points on the graph.

Alternative Method
Mode: Rad & function
Enter equation: Y1=
Press 2nd QUIT
Press VARS
Move to Y-VARS
Cursor at 1: Function, Enter
Cursor at Y1, Enter
Insert value in the domain of Y1, i.e., Y1(a), Enter
The functional value at a will appear
Repeat for other values.

NOTE: When graphing functions, make sure your plots are off in the y= menu. If not, you will get an error message.

STORING & RECALLING A GIVEN VALUE

1)  Take any number or a result of a computation you wish to store & proceed to the next step.

2)  Press  STO-> , ALPHA (blue) & any key with a small blue letter.

3)  To recall this value, press 2nd,  RCL, ALPHA, & the key where you stored the value, enter.

Note:  Storing values is very handy in complex operations where a particular complex operation is repeated several times.

DRAWING TANGENT LINES TO FUNCTIONS & GETTING THEIR EQUATIONS

Mode: Rad & function
Enter equation: y1=
Zoom 7 (this will graph equation)
2nd draw
Select 5: will get Tangent(
Enter in x-value of point
Tangent line will be drawn & equation will be given.


EQUATION SOLVER   [for solving f(x)=g(x) in the form 0=g(x)-f(x)]

Click mode to get in Func mode
Click Math
Click cursor up to Math, then click enter
Move cursor up, then click enter
Should see: Eqn: 0=
if there is another equation there, click clear
Should see Eqn: 0 =
Enter the right side of the equation (after the = sign)
Click Alpha then Enter
Enter a guess (near a solution)
Click Alpha then Enter
Solution for x is shown
repeat with another guess for other intersections

Here's how to find the MAXIMUM & MINIMUM pts using your TI-83.
Understand that these are approximations & not exact values, if
they do not come out exactly. For exact values, use the procedures
outlined in class. (most likely, you'll have to find exact values on
tests). However, the following procedure is a nice way to check your
answers.

 1)  Code in your equation at Y1.
 2)  Set your viewing window for x & y (this might have to be adjusted, if the entire curve is not visible). To set a friendly window, look at functional values (see Finding functional values, above)
 3)  click graph (graph of f should appear)
 4)  click 2nd trace
 5)  enter (3) Minimum or (4) Maximum
 6)  Enter an x value to the left of the min/max pt
 7)  Enter a value to the right of the min/max pt
 8)  enter any value between as a guess
 9)  the coordinates of your min/max pt will appear at the bottom of the window          

 (you could also just use trace & zoom to get there)

GUESSING LIMITS USING YOUR CALCULATOR

Choose values close to the limit.(on either side, when appropriate)
Calculate the value of the expression
See if the expression is getting closer to one number.

Note: There will be better ways to get the exact limit without the use of a calculator.

GRAPHING THE DERIVATIVE OF A FUNCTION
go to the y= menu to Y1=, click the MATH menu to 8, enter, then code in the equation of the function, x,x), then press graph. Make sure you have a friendly viewing window.


NUMERICAL INTEGRATION (for evaluating Definite Integrals).
First, enter your function (to be integrated) by pressing Y= (top left).
Make sure you set the proper viewing window for X. The range (Xmin to Xmax) must include the limits of integration or you will get an error message. The Graph of the function, with the shaded area in question, is not necessary to get the final answer to the definite integral.
Next, press 2nd, Trace for the Calc menu, go to menu 7, enter.
The display will prompt you to enter the lower limit of integration.
Press enter, then enter the upper limit, press enter.
The result is the numerical value corresponding to the definite integral.
It may or may not be exact, depending on the function & the limits of integration.
It represents the area between the x-axis & the function in question between those limits. It may be negative, if the area is below the axis.

~Note: Common mistakes leading to wrong answers are mostly likely associated with the improper use of parentheses, especially with calculations involving ex. Finding ex with the power key(^) will give an incorrect result unless the entire term is in parenthesis along with its power (need two sets of parentheses). So, when confronted with calculations involving ex, it is best to use the 2nd ex key directly.

~NOTE: if you're having much difficulty with your calculator & seem to be getting "junk" most of the time with all kinds of nasty messages, do the following:
click 2nd MEM ENTER
7 Reset ENTER
2 Defaults ENTER
2 Reset ENTER
Clear
This will reset you calculator
you might lose saved programs, so take note