TI-89 Tutorial Answers

Key -> Sequence      Joy pad:Option

1) Clean the machine From the HOME window
F1:Clear Home erases all expresions in the Home window.
F6:Clear a-z Enter removes all 1 letter variables.
Diamond -> Y = to mark enter the function editor, then F1:Clear Functions ->  Enter will remove all functions in the Y = editor.


2) Substitution and approximation From the HOME window
Key in the function with the following. xÙ2/3-8Ö(6yÙ3)
Continue that line and make the substitutions with the following. xÙ2/3-8Ö(6yÙ3)| x=6 and y=1/3
Evaluate with Enter. Approximate with Diamond ->  Enter

3) Solving for a variable From the HOME window
Use F2:solve( or type in solve(xÙ2/3-8Ö(6yÙ3)=0,y) followed by Enter

4) Solving a system From the HOME window
solve(4x-3y=2 and xÙ2/4-yÙ2/9=1, {x,y})
Or find the x coordinates with solve(4x-3y=2,y) followed by solve(xÙ2/4-yÙ2/9=1,x)| y=2(2x-1)/3
Find the corresponding y coordinates with y=2(2x-1)/3 | x=-2(9*Ö(21)+16)/17
and y=2(2x-1)/3 | x=-2(9*Ö(21)+16)/17.

5) Graphing a Euclidean system From the HOME window
Set the graphing mode to sketch Euclidean Â2 space by MODE:Graph:FUNCTION.
Then, solve the hyperbola for y using solve(xÙ2/4-yÙ2/9=1,y).
Use the JoyPad to highlight the solution and copy it to the buffer with F1:Copy.
Move it to the Y = editor with Diamond -> Y = and paste the solution to y1(x) with F1:Paste.
Use the JoyPad and the ¬ to set y1(x)=-3Ö(xÙ2-4)/2 and paste again and edit to set y2(x)=3Ö(xÙ2-4)/2.
Either cut and paste or use the JoyPad to set y3(x) = 2(2x-1)/3.
Plot them all with Diamond -> Graph.
Use F3 to set the trace mode and the JoyPad to control the trace cursor.
You can also use F2 to choose zoom options.

6) Derivatives and critical points From the HOME window
Either use F3:d( or 2nd -> 8 to type in d(a*xÙ3+b*xÙ2+c*x+d,x,2)followed by Enter.
Enter in solve(d(a*xÙ3+b*xÙ2+c*x+d,x)=0,x) followed by Enter.

7) Indefinite and definite integrals From the HOME window
Either by F3:ò( or 2nd -> 7 to type in ò(yÙ2 tan-1(y),y) followed by Enter.
Multiple integrals are handled by nesting, so the innermost integral is ò(rÙ2 sin(q),r,0,1)
which means that the double integral is evaluated as ò(ò(rÙ2 sin(q),r,0,1),q,p/4,p/3) followed by Enter.

8) Limits From the HOME window
Either use F3:limit( or type in limit((xÙ2-x-6)/(xÙ3-27),x,3) followed by Enter.
There's no need to use limits on infinite integrals, so ò(1/(x*ln(x)),x,1,¥)followed by Enter.

9) Parametric and polar curves
Set the graphing mode to sketch Parametric Â2 space by MODE:Graph:PARAMETRIC.
Enter the Y = editor with Diamond -> Y = and set x(t1)=3 cos(t) and y(t1)=5 sin(t).
Open up the graphing window parameters with Diamond -> Window and set tmin=-p/2 and tmax=p/2.
Graph the curve with Diamond -> Graph.
Set the graphing mode to sketch Polar Â2 space by MODE:Graph:POLAR.
Enter the Y = editor with Diamond -> Y = and set r1=3/cos(2 q).
Graph the curve with Diamond -> Graph.

10) Graphing Euclidean Â3 surfaces
Set the graphing mode to sketch Euclidean Â3 space by MODE:Graph:3D.
Enter the Y = editor with Diamond -> Y = and set z1=xÙ2-yÙ2.
Set the graphing display with F1:Format:Style:WIRE AND CONTOUR.
Graph the surface with Diamond -> Graph.
Use of the JoyPad will rotate the surface in space.

11) Solving and graphing differential equations From the HOME window
Use F3:deSolve( or just type in deSolve(y'=1/1000 y*(100-y),t,y) followed by  Enter.
To find the constant @n, use F4:Define to set the function Define y=100*eÙ(t/10)/(eÙ(t/10)+100*@n).
Then solve(y=10,@n) | t=0.  To code the @ symbol, use the 2nd:Char:Punctuation:@ menu path.
Set the graphing mode to sketch Differential Equations Â2 space by MODE:Graph:DIFF EQUATIONS.
Enter the Y = editor with Diamond -> Y = and set t0=0, y1'=.001*y1*(100-y1), and yi1=10.
Set the graphing display with F1:Format:Fields:SLPFLD.
Graph the surface with Diamond -> Graph.

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