User Manual
Page 80
Press 2 g ? 6 b 0 b 0 2 h § jd ¸2 g 4 b 0 b 2 2 h§ja¸2g?1b2 b 1 2 h §jb ¸2 g 7 b 6 b 5 2 h §jc ¸ 2. Solve (x* a+y*b+z*c=d {x,y,z}) Press „ 1 X p j a « y p j b « z p jc Á jd b2[ X b Y bZ 2\d¸ Previews 80 Finding the Integral of Functions Steps and keystrokes Display Find the integral of vectors. Input a row or column of x...sin(x) with respect to x. This example...
Press 2 g ? 6 b 0 b 0 2 h § jd ¸2 g 4 b 0 b 2 2 h§ja¸2g?1b2 b 1 2 h §jb ¸2 g 7 b 6 b 5 2 h §jc ¸ 2. Solve (x* a+y*b+z*c=d {x,y,z}) Press „ 1 X p j a « y p j b « z p jc Á jd b2[ X b Y bZ 2\d¸ Previews 80 Finding the Integral of Functions Steps and keystrokes Display Find the integral of vectors. Input a row or column of x...sin(x) with respect to x. This example...
User Manual
Page 84
... C Display 5. A one-step function is available for x in the history area. Press ¸ Í C ¸ ¸ The solution is: x = L8/11 and y = L20/11 This example is the Previews 84 Constants and Measurement Units Using the equation f = m...a, calculate the force when m = 5 ...kilograms and a = 20 meters/second2. What is the force when a = 9.8 meters/second2. (This is a demonstration of equations. Highlight the equation for solving systems of symbolic manipulation. Then substitute the value...
... C Display 5. A one-step function is available for x in the history area. Press ¸ Í C ¸ ¸ The solution is: x = L8/11 and y = L20/11 This example is the Previews 84 Constants and Measurement Units Using the equation f = m...a, calculate the force when m = 5 ...kilograms and a = 20 meters/second2. What is the force when a = 9.8 meters/second2. (This is a demonstration of equations. Highlight the equation for solving systems of symbolic manipulation. Then substitute the value...
User Manual
Page 181
... press ¸. - Note: To cancel the menu without making a selection, press N. 2. Define, edit, and select functions or equations for viewing a graph. Display graphs. Selecting an Application The graphing calculator has different applications that lists the applications. Set window dimensions for graphing. or - • Press the number or letter for that application. Application: FlashApps Y= Editor Window Editor...
... press ¸. - Note: To cancel the menu without making a selection, press N. 2. Define, edit, and select functions or equations for viewing a graph. Display graphs. Selecting an Application The graphing calculator has different applications that lists the applications. Set window dimensions for graphing. or - • Press the number or letter for that application. Application: FlashApps Y= Editor Window Editor...
User Manual
Page 182
Enter expressions and instructions, and perform calculations. Enter and edit a text session. From the Apps...you : Display a table of the application and more than one application begins with that correspond to an entered function. The application either opens directly or displays a dialog box. (Your Apps desktop may vary from the one... variable values that letter, the first one shown below.) Operating the Calculator 182 Enter and edit programs and functions. You can perform statistical calculations and graph statistical plots. Enter and edit lists, data, and matrices. Enter ...
Enter expressions and instructions, and perform calculations. Enter and edit a text session. From the Apps...you : Display a table of the application and more than one application begins with that correspond to an entered function. The application either opens directly or displays a dialog box. (Your Apps desktop may vary from the one... variable values that letter, the first one shown below.) Operating the Calculator 182 Enter and edit programs and functions. You can perform statistical calculations and graph statistical plots. Enter and edit lists, data, and matrices. Enter ...
User Manual
Page 190
... Clears all single-character variable names in the current folder (same as : solve(a¦x2+b¦x+c=0,x) If any of the variables have already been assigned a value, your calculation may produce misleading results. NewProb performs a variety of operations that let you can...Clear a-z before beginning the calculation. Single-character variable names are locked or archived. Operating the Calculator 190 Menu Item Clear a-z NewProb Restore custom default Notes: Description Clears (deletes) all functions and stat plots (FnOff and PlotsOff) in the current graphing mode. • Performs ...
... Clears all single-character variable names in the current folder (same as : solve(a¦x2+b¦x+c=0,x) If any of the variables have already been assigned a value, your calculation may produce misleading results. NewProb performs a variety of operations that let you can...Clear a-z before beginning the calculation. Single-character variable names are locked or archived. Operating the Calculator 190 Menu Item Clear a-z NewProb Restore custom default Notes: Description Clears (deletes) all functions and stat plots (FnOff and PlotsOff) in the current graphing mode. • Performs ...
User Manual
Page 231
...the normal menu returns. For example, from the calculator Home screen's normal toolbar menu, press 2 ½ to solving equations. Unless the menu has been modified, the default custom menu appears. Function names such as _m, _ft, and _l. Calculator Home Screen 231 Items related to toggle the ...custom menu on and off. 2 ¾ Calculator Home screen normal toolbar menu Custom ...
...the normal menu returns. For example, from the calculator Home screen's normal toolbar menu, press 2 ½ to solving equations. Unless the menu has been modified, the default custom menu appears. Function names such as _m, _ft, and _l. Calculator Home Screen 231 Items related to toggle the ...custom menu on and off. 2 ¾ Calculator Home screen normal toolbar menu Custom ...
User Manual
Page 240
..., and Auto Modes The Exact/Approx mode settings, which the TI-89 Titanium calculates a result. For example, 12 transforms to 2 3 and ln(1000) transforms to 3 ln(10). • Converts floating-point numbers to standard forms as much as possible without approximating them. The functions solve, cSolve, zeros, cZeros, factor, ‰, fMin, and fMax use only...
..., and Auto Modes The Exact/Approx mode settings, which the TI-89 Titanium calculates a result. For example, 12 transforms to 2 3 and ln(1000) transforms to 3 ln(10). • Converts floating-point numbers to standard forms as much as possible without approximating them. The functions solve, cSolve, zeros, cZeros, factor, ‰, fMin, and fMax use only...
User Manual
Page 242
Functions such as solve and ‰ (integrate) can use less memory than the EXACT ... more compact and comprehensible than exact results. Approximate results are rational numbers. Results with undefined variables or functions often exhibit incomplete cancellation. Symbolic operations such as 1.23457E-11. Otherwise, floating-point arithmetic is used ...after Symbolic Manipulation 242 If you may prefer to see 1/7 instead of .142857. These functions skip all of their exact symbolic techniques in the APPROXIMATE setting. For example, you do not plan to ...
Functions such as solve and ‰ (integrate) can use less memory than the EXACT ... more compact and comprehensible than exact results. Approximate results are rational numbers. Results with undefined variables or functions often exhibit incomplete cancellation. Symbolic operations such as 1.23457E-11. Otherwise, floating-point arithmetic is used ...after Symbolic Manipulation 242 If you may prefer to see 1/7 instead of .142857. These functions skip all of their exact symbolic techniques in the APPROXIMATE setting. For example, you do not plan to ...
User Manual
Page 243
...-point infection does not leap over barriers such as undefined variables or between elements of a result by choosing to {1/6, .16666666666667} In the AUTO setting, functions such as solve determine as many solutions as either rational or floating-point numbers. Advantages Disadvantages You see exact results when practical, and approximate numeric results when...
...-point infection does not leap over barriers such as undefined variables or between elements of a result by choosing to {1/6, .16666666666667} In the AUTO setting, functions such as solve determine as many solutions as either rational or floating-point numbers. Advantages Disadvantages You see exact results when practical, and approximate numeric results when...
User Manual
Page 247
...solve(x^2NxN2=0,x) d(x^2NxN2,x) ‰(x^2NxN2,x) limit(x2NxN2,x,5) For a function that value is simplified to the lowest level at least two arguments with respect to a variable. The function is performed. If var can be further simplified to a function. The var variable is then substituted into the result. For certain functions... uses delayed simplification: 1. Symbolic Manipulation 247 Delayed Simplification for Certain Built-In Functions Usually, variables are automatically simplified to their lowest possible level before they are passed to a non-variable value). 2. ...
...solve(x^2NxN2=0,x) d(x^2NxN2,x) ‰(x^2NxN2,x) limit(x2NxN2,x,5) For a function that value is simplified to the lowest level at least two arguments with respect to a variable. The function is performed. If var can be further simplified to a function. The var variable is then substituted into the result. For certain functions... uses delayed simplification: 1. Symbolic Manipulation 247 Delayed Simplification for Certain Built-In Functions Usually, variables are automatically simplified to their lowest possible level before they are passed to a non-variable value). 2. ...
User Manual
Page 253
... logarithms are valid for more general expressions (either møc2=e or c2øm=e) may not work as you anticipate. Symbolic Manipulation 253 Note: Use the solve function to specify the domain constraint. No match for substitution Specifying Domain Constraints Many identities and transformations are not combined. Because ln(x†y) = ln(x) + ln(y) is...
... logarithms are valid for more general expressions (either møc2=e or c2øm=e) may not work as you anticipate. Symbolic Manipulation 253 Note: Use the solve function to specify the domain constraint. No match for substitution Specifying Domain Constraints Many identities and transformations are not combined. Because ln(x†y) = ln(x) + ln(y) is...
User Manual
Page 256
.... Displays in an expression and transforms the expression into a reduced ratio of each function and its variables or with respect to the Technical Reference module. Calculates a common denominator for a specified variable. Symbolic Manipulation 256 Evaluates an expression using 8 ¸ to solve, which may display several solutions in a rational or symbolic form). Menu Item...
.... Displays in an expression and transforms the expression into a reduced ratio of each function and its variables or with respect to the Technical Reference module. Calculates a common denominator for a specified variable. Symbolic Manipulation 256 Evaluates an expression using 8 ¸ to solve, which may display several solutions in a rational or symbolic form). Menu Item...
User Manual
Page 257
... inequality. left -hand side of tExpand. getDenom - Applies comDenom and then returns the resulting denominator. Displays the submenu: Extract These are the same as solve, factor, and zeros; Displays the submenu: getNum - Applies comDenom and then returns the resulting numerator. Symbolic Manipulation 257 Returns the left - Expands trig ... sums and multiple angles. Menu Item Trig Description Displays the submenu: Complex tExpand - TCollect - Collects the products of integer powers of trig functions into angle sums and multiple angles. but they also compute complex results.
... inequality. left -hand side of tExpand. getDenom - Applies comDenom and then returns the resulting denominator. Displays the submenu: Extract These are the same as solve, factor, and zeros; Displays the submenu: getNum - Applies comDenom and then returns the resulting numerator. Symbolic Manipulation 257 Returns the left - Expands trig ... sums and multiple angles. Menu Item Trig Description Displays the submenu: Complex tExpand - TCollect - Collects the products of integer powers of trig functions into angle sums and multiple angles. but they also compute complex results.
User Manual
Page 260
Finding Partial Expansions With the expand („ 3) function's optional var value, you can do a partial expansion with respect to all variables. Do a full expansion of a variable. solve(equation, var) Solve x + y N 5 = 2x N 5y for a specified variable. Solving an Equation Use the solve („ 1) function to x. Symbolic Manipulation 260 Notice that collects similar powers of (x2Nx) (y2Ny) with respect to solve an equation for x. Then do a partial expansion that solve displays only the final result.
Finding Partial Expansions With the expand („ 3) function's optional var value, you can do a partial expansion with respect to all variables. Do a full expansion of a variable. solve(equation, var) Solve x + y N 5 = 2x N 5y for a specified variable. Solving an Equation Use the solve („ 1) function to x. Symbolic Manipulation 260 Notice that collects similar powers of (x2Nx) (y2Ny) with respect to solve an equation for x. Then do a partial expansion that solve displays only the final result.
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... following methods. Substitutions are in the Previews chapter, which solved for a one-step solve(2xN3y=4 and Lx+7y=L12,{x,y}) solution. Use the solve function with two unknowns: 2x N 3y = 4 Lx + 7y = L12 To solve this system of equations, use any of an equality, ...such as | 2 p subtracts 2x from both sides. Method Example Use the solve function for x = L8/11 and y = L20/11. Symbolic Manipulation 261 To see intermediate results, you can manually solve the equation step-by -step manipulation. x « y | 5 Á 2x | 5y | 2 x ...
... following methods. Substitutions are in the Previews chapter, which solved for a one-step solve(2xN3y=4 and Lx+7y=L12,{x,y}) solution. Use the solve function with two unknowns: 2x N 3y = 4 Lx + 7y = L12 To solve this system of equations, use any of an equality, ...such as | 2 p subtracts 2x from both sides. Method Example Use the solve function for x = L8/11 and y = L20/11. Symbolic Manipulation 261 To see intermediate results, you can manually solve the equation step-by -step manipulation. x « y | 5 Á 2x | 5y | 2 x ...
User Manual
Page 404
... plot is not unique for each x, so you cannot graph this increases the graph evaluation time. • When you cannot explicitly solve for y in function graphing mode. y is a 3D contour plot with a single contour drawn for x in function graphing mode. 3D Graphing 404 Explicit and Implicit Forms In 2D function graphing mode, equations have an implicit form f(x,y)=g(x,y), where you animate...
... plot is not unique for each x, so you cannot graph this increases the graph evaluation time. • When you cannot explicitly solve for y in function graphing mode. y is a 3D contour plot with a single contour drawn for x in function graphing mode. 3D Graphing 404 Explicit and Implicit Forms In 2D function graphing mode, equations have an implicit form f(x,y)=g(x,y), where you animate...
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... them as parametric equations. • Break them into separate, explicit functions. Notes: You can also graph many implicit forms if you can graph these implicit forms without solving for y or x. Display the GRAPH FORMATS dialog box from the Y= Editor, Window editor, or Graph screen: 8Í 3D Graphing 405 In the Y= Editor, enter the non-zero side of...
... them as parametric equations. • Break them into separate, explicit functions. Notes: You can also graph many implicit forms if you can graph these implicit forms without solving for y or x. Display the GRAPH FORMATS dialog box from the Y= Editor, Window editor, or Graph screen: 8Í 3D Graphing 405 In the Y= Editor, enter the non-zero side of...
User Manual
Page 444
20. Differential Equation Graphing 444 to xc = 40, you solve many 1st- RK (Plot 1) Exact solution (y1) y1 is selected when 1 shows here By moving the trace cursor to trace each solution to trace, and ...: • The exact solution (y1) is 85.8486, rounded to time = 40. and 2nd-order ordinary differential equations exactly. Press ... Example of the deSolve( ) Function The deSolve( ) function lets you can also use the Data/Matrix Editor to open the errorlog data variable and scroll to six digits. • The RK solution...
20. Differential Equation Graphing 444 to xc = 40, you solve many 1st- RK (Plot 1) Exact solution (y1) y1 is selected when 1 shows here By moving the trace cursor to trace each solution to trace, and ...: • The exact solution (y1) is 85.8486, rounded to time = 40. and 2nd-order ordinary differential equations exactly. Press ... Example of the deSolve( ) Function The deSolve( ) function lets you can also use the Data/Matrix Editor to open the errorlog data variable and scroll to six digits. • The RK solution...
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Page 446
... 3. Note: If you got a different constant (@2, etc.), solve for that constant. @1 represents a constant. For @, type @ 89 H 2R Differential Equation Graphing 446 Use the solution to highlight the solution in the history ...area. Then press ¸. Note: Press 2 A to move to find the general solution. 2. a) Press C to define a function. You may get a different constant (@2, etc.). Before using deSolve( ), clear any existing t and y variables. In the Home screen @ " "use solve...
... 3. Note: If you got a different constant (@2, etc.), solve for that constant. @1 represents a constant. For @, type @ 89 H 2R Differential Equation Graphing 446 Use the solution to highlight the solution in the history ...area. Then press ¸. Note: Press 2 A to move to find the general solution. 2. a) Press C to define a function. You may get a different constant (@2, etc.). Before using deSolve( ), clear any existing t and y variables. In the Home screen @ " "use solve...
User Manual
Page 667
... the system variable eqn. For example, a(m2+m1) is set equal to a function or equation defined elsewhere. Type an expression without an = sign. e+fNln(g) After you defined y1(x) on either define exp or solve for it. Numeric Solver 667 or - • Home screen: Define y1(x)=1.25x...8226; Be careful with implied multiplication. You can either the: • Y= Editor: y1(x)=1.25x†cos(x) - Notes: • Do not use system function names (such as y1(x) or r1(q)) as : exp=e+fNln(g) Recall a previously entered equation or open a saved equation. Suppose you press ¸, the ...
... the system variable eqn. For example, a(m2+m1) is set equal to a function or equation defined elsewhere. Type an expression without an = sign. e+fNln(g) After you defined y1(x) on either define exp or solve for it. Numeric Solver 667 or - • Home screen: Define y1(x)=1.25x...8226; Be careful with implied multiplication. You can either the: • Y= Editor: y1(x)=1.25x†cos(x) - Notes: • Do not use system function names (such as y1(x) or r1(q)) as : exp=e+fNln(g) Recall a previously entered equation or open a saved equation. Suppose you press ¸, the ...