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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 x2 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 x2 x 2 lim 1 x 2 , x, 2, 1 Note: The 1 at the end can be any negative number. 1 4) lim x2 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