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TI89 and Voyage 200

TI89 and Voyage 200. Student Support Services Presented by Andy Williamson and Amanda Griffin. Showing Computations. Compute sin( π /4)and display the result in symbolic and numeric format. To clear the history area of previous calculations, press F1 and select 8:Clear Home.

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TI89 and Voyage 200

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  1. TI89 and Voyage 200 Student Support Services Presented by Andy Williamson and Amanda Griffin

  2. Showing Computations Compute sin(π/4)and display the result in symbolic and numeric format. To clear the history area of previous calculations, press F1 and select 8:Clear Home. Press π÷ 4[≈] 2nd ) SIN ENTER 

  3. Showing Computations

  4. Finding the Factorial of Numbers Compute the factorial of several number to see how the TI89/Voyage 200 handles very large integers. To get the factorial operator (!) press [MATH], select 7:Probability, and then select 1:! Press 5 [!] 20 [!] 30 [!] 2nd 2nd 2nd 2nd ENTER ENTER ENTER

  5. Finding the Factorial of Numbers

  6. Expanding Complex Numbers Compute (3+5i)³ to see how the TI89/Voyage 200 handles computations involving complex numbers. Press 3 5 [i ] 3 ( + 2nd ) ^ ENTER

  7. Expanding Complex Numbers

  8. Finding Prime Factors Compute the factors of the rational number 2634492. You can enter “factor” on the entry line by typing FACTOR on the keyboard, or by pressing and selecting 2: factor(. Press 2 2634492 F2 F2 ) ENTER

  9. Finding Prime Factors

  10. Finding Roots Find the root of the expression (x,y). You can enter “root” on the entry line by typing ROOT on the keyboard, or by pressing 9. This example illustrates using the root function and how the expression is displayed in “pretty print” in the history area. Press 9 X Y  , )  ENTER

  11. Finding Roots

  12. Expanding Expressions Expand the expression (x-5)³. You can enter “expand” on the entry line by typing EXPAND on the keyboard, or by pressing and selecting 3:expand(. Press 3 X 5 3 F2 F2 ( - ) ^ ) ENTER

  13. Expanding Expressions

  14. Reducing Expressions Reduce the expression (x²-2x-5)/(x-1) to its simplest form. You can enter “propFrac” on the entry line by typing PROPRAC on the keyboard, or by pressing and selecting 7:propFrac(. Press 7 X 2 2 X 5 X 1 F2 F2 ^ ) ÷ ( - - ( ) ) - ENTER

  15. Reducing Expressions

  16. Factoring Polynomials Factor the polynomial (x²-5) with respect to x. You can enter “factor” on the entry line by typing FACTOR on the keyboard or by pressing and selecting 2:factor(. Press 2 X 2 5 X F2 F2 ^ ) - , ENTER

  17. Factoring Polynomials

  18. Solving Equations Solve the equation x²-2x-6=2 with respect to x. You can enter “solve(“ on the entry line by selecting “solve(“ from the Catalog menu, by typing SOLVE( on the keyboard, or by pressing and selecting 1:solve(. The status line area shows the required syntax for the marked item in the Catalog menu. Press 1 X 2 2 X 6 2 X F2 F2 ^ - - = , ) ENTER

  19. Solving Equations

  20. Solving Equations with a Domain Constraint Solve the equation x²-2x-6=2 with respect to x where x is greater than zero. The “with” (l) operator provides domain constraint. Press 1 x 2 2 x 6 2 x [l] x [>] 0 F2 ^ ) - - = , 2nd 2nd ENTER

  21. Solving Equations with a Domain Constraint

  22. Solving inequalities Solve the inequality (x²>1,x) with respect to x. Press 1 x 2 [>] 1 x ) F2 ^ 2nd , ENTER

  23. Solving inequalities

  24. Find the Derivative of Functions Find the derivative of (x-y)³/(x+y)² with respect to x. This example illustrates using the calculus differentiation function and how the function is displayed in “pretty print” in the history area. Press [d] x y 3 x y 2 x ÷ ( - ) ^ ( + 2nd ) ) ^ , ENTER

  25. Find the Derivative of Functions

  26. Finding Implicit Derivatives Compute implicit derivatives for equations in two variables in which one variable is defined implicitly in terms of another. This example illustrates using the calculus implicit derivative function. Press D x 2 y 2 100 x y ^ + ^ = , , F3 ) ENTER

  27. Finding Implicit Derivatives

  28. Finding the Integral of Functions Find the integral of x*sin(x) with respect to x. This example illustrates using the calculus integration function. Press [∫] x x x x ( ) ) 2nd SIN , ENTER

  29. Finding the Integral of Functions

  30. Solving Problems Involving Vectors • Input a row or column of vectors. Press [ [ ] 6 0 0 [ ] ] d [ [ ] 4 0 2 [ ] ] a [ [ ] 1 2 1 [ ] ] b [ [ ] 7 6 5 [ ] ] c (-) 2nd , , 2nd STO ► ENTER 2nd , , 2nd STO ► (-) , , 2nd STO ► ENTER 2nd 2nd , , 2nd STO ► ENTER ENTER

  31. Solving Problems Involving Vectors Cont. 2 Solve (x *a+y*b+z*c=d {x,y,z}) Press 1 x a y b z c d [(] x y z [)] x x F2 + x + = , 2nd , , 2nd ) ENTER

  32. Solving Problems Involving Vectors Cont.

  33. Symbolic Manipulation Solve the system of equations 2x-3y=4 and -x+7y=-12. solve the first equation so the x is expressed in terms of y. Substitute the expression for x into the second equation, and solve for the value of y. Then substitute the y value back into the first equation to solve for the value of x.

  34. Symbolic Manipulation Cont. • Display the Home screen and clear the entry line. Solve the equation 2x-3y=4 for x. 1 selects solve( from the Algebra menu. You can also type solve( directly from the keyboard or select if from the Catalog. Press [CALC HOME] 1 2 X 3 Y 4 x F2 CLEAR CLEAR F2  ) - = , ENTER

  35. Symbolic Manipulation Cont. 2. Begin to solve the equation –x+ 7y=-12 for y, but do not press yet. Press 1 x 7 Y 12 Y ENTER (-) ) F2 (-) + = ,

  36. Symbolic Manipulation Cont. 3. Use the “with” operator to substitute the expression for x that was calculated from the first equation. This gives the value of y. The “with” operator is displayed as l on the screen. Use the auto-pate feature to highlight the last answer in the history area and paste it to the entry line. Press [l] ▲ 2nd ENTER ENTER

  37. Symbolic Manipulation Cont. 4. Highlight the equation for x in the history area. Press ▲ ▲ ▲

  38. Symbolic Manipulation Cont. 5. Auto-paste the highlighted expression to the entry line. Then substitute the value of y that was calculated from the second equation. Press [l] The solution is: X=-8/11 and y=-20/11 This example is a demonstration of symbolic manipulation. A one-step function is available fro solving systems of equations. 2nd ▲ ENTER ENTER ENTER

  39. Symbolic Manipulation Cont.

  40. Basic Function Graphing I The example in this section demonstrates some of the graphing capabilities of the TI/89/Voyage 200 keystrokes. It illustrates how to graph a function using the Y=Editor. You will learn how to enter a function, produce a graph of the function, trace a curve, find a minimum point, and transfer the minimum coordinates to the Home screen. Explore the graphing capabilities of the TI-89/Voyage 200 by graphing the function y=(|x²-3|-10)/2.

  41. Basic Function Graphing I Cont. • Display the Y=Editor. Press [Y=] 2. Enter the function (abs(x²-3)-10)/2 The screen shot shows the “pretty print” display at y1= Press [CATALOG] A x 2 3 10 2  ^ ) ( 2nd ENTER - - ) ÷ ENTER

  42. Basic Function Graphing I Cont. 3.Display the graph of the function Select 6: ZoomStd by pressing 6 or by moving the cursor to 6:ZoomStd and Pressing Press 6 ENTER F2

  43. Basic Function Graphing I Cont.

  44. Basic Function Graphing I Cont. 4. Turn on Trace. The tracing cursor, and the x and y coordinates are displayed. Press F3

  45. Basic Function Graphing I Cont. 5. Open the MATH menu and select 3: Minimum. Press ▼ ▼ F5 ENTER

  46. Basic Function Graphing I Cont. 6. Set the lower bound. Press (right cursor) to move the tracing cursor until the lower bound for x is just to the left of the minimum node before pressing the second time. Press … ► ENTER ► ► ENTER

  47. Basic Function Graphing I Cont.

  48. Basic Function Graphing I Cont. 7. Set the upper bound. Press (right cursor) to move the tracing cursor until the upper bound for x is just to the right of the minimum node. Press … ► ► ►

  49. Basic Function Graphing I Cont.

  50. Basic Function Graphing I Cont. 8. Find the minimum point on the graph between the lower and upper bounds. Press ENTER

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