Calculus on the Ti-89

CALCULUS ON THE TI-89

If you set your calculator to Automatic mode:

To get the exact answer, just press Enter. To get a decimal answer, press Green Diamond Enter.

ProblemCalculator Syntax Answer

1) 5

2)

Note: The 1 at the end can be any positive number.

3)

Note: The 1 at the end can be any negative number.

4) undef

5)

6) e

7) If

find .Note: If you enter , you would

get the second derivative. A 3 at the end

would give the third derivative, etc.

8) If

find .

Note: The vertical segment means “when.” It is found on the keyboard right above the EE key.

9) Find the derivative of

10) Find the derivative of . Then comDenom(Answer)

11) Find the equation of the tangent line Put into y1 and graph. Then F5 Tangent 1 Enter

to at x = 1 Answer is

12) Find given . Go to F3 and select impDiff.

impDiff

To evaluate at the point , capture your previous answer from the history area, and use

the “when” key to type in the values: . Your answer should be – 1.

13)

14)

15) Put into y1 and graph. Then F5 7 -1 Enter 3 Enter

Answer is 4

16)

17) Solve: deSolve

Note: You must put a times sign between the x

and y terms.

18) Solve: deSolve

and Note: “and” is in the Catalog. It gives a space, then

“and” followed by another space, which is what

you need.

19) Graph a slope field for Put the calculator in Differential Equations mode. Let.

. Use a Zoom 4 window, and change the fldres to 15.

Note: You must use t instead of x and y1 instead of y.

20) Graph a slope field for Same as directions for 13) but also let t0 = 1 and yi1 =

and . OR leave yi1 blank, graph the slope field, and then press F8. The screen will ask you for t and for y1. Enter 1 for t and

for y1.

21) Use Euler’s method to First graph the slope field with the initial condition, as shown in

estimate , the directions for 13). Then press the green diamond key,

given , followed by the “when” key (vertical segment right above the

and “EE” key) to get to the Format Screen. Go down to Solution

Method and choose Euler. (This sets the calculator to do Euler’s

Method, rather than the Runge-Kutta method.) Then go to y =

and let t0 = 1 and yi1 = . Go to the Window, and let the

tstep = 0.5. Then press green diamond F3, and the solution

curve will be drawn with the given initial condition and

step-size. Press “Trace” to see the solutions given by Euler’s

method. The solutions can also be viewed in the Table if you

go to TblSet and let tblStart = 1 and tbl = 0.5. You should

get

22) 1.54976…

23) Find a Taylor polynomial TaylorOR Taylor

of degree 4 for ,

centered at 0. Note: By default, the calculator will center the polynomial at 0

unless you enterthe center at the end of the command.