Download calculus on the ti-89 - andrea

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.
Home Screen (no menus)
problem
result
tan-1(∞)
e ^ (-∞)
e ^ (π i)
ln (0)
π/2
0
-1
-∞
Problem
1) lim  x  3
Calculator Syntax
lim  x  3, x, 2
 1 
2) lim 

x2  x  2 
lim 1   x  2 , x, 2, 1
x 2
Answer
5

Note: The 1 at the end can be any positive number.
3)
 1 
lim 

x2  x  2 
lim 1   x  2 , x, 2, 1

Note: The  1 at the end can be any negative number.
 1 
4) lim 
x2  x  2 

lim 1   x  2 , x, 2
 5x  3 
5) lim 
x   4 x  1 

lim   5x  3   4 x 1 , x,  
5
4
lim  1  1/ x  ^ x, x, 
e
 1
6) lim 1  
x  
x
x
7) If f  x   cos  3x  ,
find f   x  .
d  cos  3x  , x 
Note: If you enter d  cos  3x  , x, 2 , you would
get the second derivative. A 3 at the end
would give the third derivative, etc.
undef
 3sin  3x 
8) If f  x   cos  3x  ,
 
find f    .
6
d  cos  3x  , x  x 

6
Note: The vertical segment means “when.” It is
found on the keyboard right above the EE key.
3
d
d
( f ( x)) g ( x)  ( g ( x)) f ( x)
dx
dx
9) Find the derivative of f ( x) g ( x) d  f ( x) g ( x), x 
10) Find the derivative of
f  x
.
g  x
d  f ( x)  g ( x), x 
Then comDenom(Answer)
d
d
f  x  g  x  

 g  x  f  x 
dx
dx
2
 g  x 
11) Find the equation of the tangent line
to y  x3  2 x  2 at x = 1
Put x3  2 x  2 into y1 and graph. Then F5 Tangent 1 Enter
Answer is y  x  4
12) Implicit differentiation can be done by creating a script based on Green’s Formula. On the home
screen, type: d  f , x   d  f , y  store imp  f  . Next you would take an implicitly defined
function and move all of the terms to one side. Then type: imp ( function) Enter.
For the curve defined by 2 y 3  6 x 2 y  12 x 2  6 y  1 , enter imp 2y3  6 x 2  y  12 x 2  6 y  1 .
2 x  y  2 


dy
 1 1
at the point   ,  , capture your previous
dx
x  y 1
 2 2
answer from the history area, and use the “when” key to type in the values:
2 x  y  2 
1
1
x
and y  . Your answer should be – 1 .
2
2
2
2
x  y 1
The answer should be
13)
2
 x dx
1
14)

15)
3
  x  2 x  2  dx
0
x 2 dx
3
1
2
2
. To evaluate
  x  2, x 
x3
3
  x  2,
1
3
x, 0, 1
Put x3  2 x  2 into y1 and graph. Then F5 7 -1 Enter 3 Enter
Answer is 4
16)

1
1
dx
x 1
2
17) Solve:
dy
 3x 2 y
dx
 1   x
2

 1 , x, 1, 

4

deSolve  y  3x  2  y, x, y 
3
y  Ce x
Note: You must put a times sign between the x
and y terms.
18) Solve:
dy
 3 x 2 y and y  0  5
dx
deSolve  y  3x  2  y and y  0  5, x, y 
Note: “and” is in the Catalog. It gives a space, then
“and” followed by another space, which is what
you need.
3
y  5e x
Put the calculator in Differential Equations mode. Let y1  t  y1 .
19) Graph a slope field for
dy
 x y.
dx
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
dy
 x  y and y 1  1 .
dx
Same as directions for 13) but also let t0 = 1 and yi1 = 1
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
1 for y1.
21) Use Euler’s method to
estimate y  2  ,
First graph the slope field with the initial condition, as shown in
the directions for 13). Then press the green diamond key,
dy
 x y,
dx
y 1  1 and x  0.5.
followed by the “when” key (vertical segment right above the
given
10
22)
“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 = 1 . 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 y 1.5  1 and y  2   0.75.
1
1  x  2, x, 1, 10
 x2
x 1
23) Find a Taylor polynomial
of degree 4 for f  x   e ,
3x
centered at 0.
1.54976…
Taylor  e   3x  , x, 4 OR Taylor  e   3x  , x, 4,0
x 2 x3 x 4
1 x   
2! 3! 4!
Note: By default, the calculator will center the polynomial at 0
unless you enter the center at the end of the command.
Susan Cinque and Nancy Stephenson, Clements High School, Sugar Land, Texas