TI Hints

Andy Long

1. Use solve to find a solution to an equation: e.g.

   

2. Use expand to expand out a function: e.g.

   

   or

   

   (expands in terms of x by default). If you want the expansion in terms of a, then you would type

   

   which would give

   

   Note:

   

   

   

   The coefficients of each term come from Pascal's triangle:

   

   Etc.!

3. TI hint: Use factor to factor an expression: e.g.

   

   Factor will try to create linear terms in x (by default), i.e.

   

4. To differentiate an expression, use the d command (from the calc menu): e.g.

   

   returns . I personally prefer to define a function in the ``Y='' menu, e.g.

   

   and then use

   

   If you have to use a function over and over, it's usually smart to define it in a way that will be stored for future use.

   Now we can do things like solve for where the derivative is zero:

   

5. The tExpand command (available from the Algebra -> trig menu) is useful for expanding out trigonometric expressions:

   

   for example yields , one of the most important trig identities.

   

   yields another: .

6. To make a sum, use the key (2nd-4 on a TI-92; F3-4 on a TI-89). As usual I do this in ``Y='' menu, e.g.

   

   This command would represent the sum

   

   which is similar to the type of sum we need when creating Riemann sums.

7. Use lists whenever possible. For example, for problem #4, p. 71, we need a slope computed for a list of domain values. You can:
   • save the domain values in a list a:

     

     (the refers to the store button (STO).

   • save the function values in a list b:

     

     Then compute the slopes as a list m:

     

     Finally, you can plot all these secant lines simultaneously by going into your ``Y='' menu, and adding the functions y1(x)=1/x and then

     

     (which is actually a family of functions corresponding to the many values of m), and you'll have a nice plot. A good window size is xmin=.25, xmax=2.5, ymin=0, ymax=3.