User Manual
Page 80
... Functions Steps and keystrokes Display Find the integral of vectors. 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 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 §...; 2. Press 2 < X p 2 W X d b X d ¸ Solving Problems Involving Vectors Steps and keystrokes Display 1. Input a row or column of x...sin(x) with respect to x. This example illustrates using the calculus integration function.
... Functions Steps and keystrokes Display Find the integral of vectors. 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 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 §...; 2. Press 2 < X p 2 W X d b X d ¸ Solving Problems Involving Vectors Steps and keystrokes Display 1. Input a row or column of x...sin(x) with respect to x. This example illustrates using the calculus integration function.
User Manual
Page 242
...rational arithmetic wherever all or some of .142857. If you may prefer to familiar, traditional numeric calculators. Symbolic operations such as limits and integration are sometimes less compact and comprehensible than exact results. Results with undefined variables or functions often exhibit...Approximate results are less likely to give satisfying results in the APPROXIMATE setting. Functions such as solve and ‰ (integrate) can use symbolic computations, approximate results are sometimes more compact and comprehensible than exact results. Approximate results are similar...
...rational arithmetic wherever all or some of .142857. If you may prefer to familiar, traditional numeric calculators. Symbolic operations such as limits and integration are sometimes less compact and comprehensible than exact results. Results with undefined variables or functions often exhibit...Approximate results are less likely to give satisfying results in the APPROXIMATE setting. Functions such as solve and ‰ (integrate) can use symbolic computations, approximate results are sometimes more compact and comprehensible than exact results. Approximate results are similar...
User Manual
Page 243
... results, some time may be wasted seeking exact results. If you might exhaust the memory seeking those exact results. Moreover, you are impractical. Similarly, ä (integrate) uses approximate numerical methods if appropriate where exact symbolic methods fail. You can often control the format of lists or matrices. For example: (1/2 - 1/3) x + (0.5 - 1/3) y transforms to...
... results, some time may be wasted seeking exact results. If you might exhaust the memory seeking those exact results. Moreover, you are impractical. Similarly, ä (integrate) uses approximate numerical methods if appropriate where exact symbolic methods fail. You can often control the format of lists or matrices. For example: (1/2 - 1/3) x + (0.5 - 1/3) y transforms to...
User Manual
Page 266
... equations, with respect to a specified variable. Evaluates an expression at discrete variable values within a range and then calculates the sum. Evaluates an expression at discrete variable values within a range and then calculates the product. Calculates an integral as a floating-point number using quadrature (an approximation using weighted sums of a specified variable that maximize an...
... equations, with respect to a specified variable. Evaluates an expression at discrete variable values within a range and then calculates the sum. Evaluates an expression at discrete variable values within a range and then calculates the product. Calculates an integral as a floating-point number using quadrature (an approximation using weighted sums of a specified variable that maximize an...
User Manual
Page 267
To get d, use ... 1 or 2 =. Differentiate the answer with respect to x. Integrating and Differentiating Use the ‰ integrate (... 2) and d differentiate (... 1) functions. ‰ (expression, var [,low] [,up]) lets you specify limits or a constant of the functions available ...section gives examples for differentiate is not the same as typing the letter D on the keyboard. Note: The d symbol for some of integration d (expression, var [,order]) Integrate x2†sin(x) with respect to the Technical Reference module. Use ... 1 or 2 =. It is a special symbol. Do not ...
To get d, use ... 1 or 2 =. Differentiate the answer with respect to x. Integrating and Differentiating Use the ‰ integrate (... 2) and d differentiate (... 1) functions. ‰ (expression, var [,low] [,up]) lets you specify limits or a constant of the functions available ...section gives examples for differentiate is not the same as typing the letter D on the keyboard. Note: The d symbol for some of integration d (expression, var [,order]) Integrate x2†sin(x) with respect to the Technical Reference module. Use ... 1 or 2 =. It is a special symbol. Do not ...
User Manual
Page 268
Note: You can differentiate an expression, list, or matrix. limit(expression, var, point [,direction]) negative number = from left positive number= from right omitted number or 0 = both Find the limit of sin(3x) / x as x approaches 0. you can find a limit for an expression, list, or matrix. Symbolic Manipulation 268 Finding a Limit Use the limit (... 3) function. Note: You can integrate an expression only;
Note: You can differentiate an expression, list, or matrix. limit(expression, var, point [,direction]) negative number = from left positive number= from right omitted number or 0 = both Find the limit of sin(3x) / x as x approaches 0. you can find a limit for an expression, list, or matrix. Symbolic Manipulation 268 Finding a Limit Use the limit (... 3) function. Note: You can integrate an expression only;
User Manual
Page 272
When: x < 0 x | 0 Use expression: Lx 5 cos(x) • If you may be able to create a multi-statement user-defined function with two pieces. For example, consider a piecewise function with the form: Func If x In some cases, you were to create an equivalent single-statement function.
When: x < 0 x | 0 Use expression: Lx 5 cos(x) • If you may be able to create a multi-statement user-defined function with two pieces. For example, consider a piecewise function with the form: Func If x In some cases, you were to create an equivalent single-statement function.
User Manual
Page 273
Define y1(x)=when(x • Create an equivalent single-statement user-defined function. Note: To select ‰ from the Calc toolbar menu, press ... 2 (or press 2 < on the keyboard). Use the TI-89 Titanium's built-in when function. Then integrate y1(x) with respect to x.
Define y1(x)=when(x • Create an equivalent single-statement user-defined function. Note: To select ‰ from the Calc toolbar menu, press ... 2 (or press 2 < on the keyboard). Use the TI-89 Titanium's built-in when function. Then integrate y1(x) with respect to x.
User Manual
Page 331
...second derivative changes sign (where the curve changes concavity). Basic Function Graphing 331 Overview of two functions. Finds a zero (x-intercept), minimum, or maximum point within an interval. Finds the approximate numerical integral over an interval. Finds the derivative (slope) at a specified... x value. Finds the intersection of the Math Menu Press ‡ from the Graph screen. Finds the inflection point of a curve, where its...
...second derivative changes sign (where the curve changes concavity). Basic Function Graphing 331 Overview of two functions. Finds a zero (x-intercept), minimum, or maximum point within an interval. Finds the approximate numerical integral over an interval. Finds the derivative (slope) at a specified... x value. Finds the intersection of the Math Menu Press ‡ from the Graph screen. Finds the inflection point of a curve, where its...
User Manual
Page 332
...xmax. Derivatives, integrals, distances, etc., are stored in system variables xc and yc (rc and qc if you press A or B, the free-moving cursor appears. Math Tool Shade Description Depends on the first function selected in the Y= Editor, and its coordinates are displayed. From the Graph screen, press...value. You may not be able to move the cursor between any two functions within an interval. Note: For Math results, cursor coordinates are graphed, this shades the function's area above or below the x axis. • If two or more functions are stored in the system variable sysMath...
...xmax. Derivatives, integrals, distances, etc., are stored in system variables xc and yc (rc and qc if you press A or B, the free-moving cursor appears. Math Tool Shade Description Depends on the first function selected in the Y= Editor, and its coordinates are displayed. From the Graph screen, press...value. You may not be able to move the cursor between any two functions within an interval. Note: For Math results, cursor coordinates are graphed, this shades the function's area above or below the x axis. • If two or more functions are stored in the system variable sysMath...
User Manual
Page 334
...Typing x values is displayed. Set the derivative point. The cursor moves to the point or type its coordinates are displayed. Finding the Numerical Integral over an Interval 1. A 4 at a Point 1. y2(x)=2xN7 Finding the Derivative (Slope) at the top of the screen marks the lower...cursor to the intersection, and its x value. 4. 5. From the Graph screen, press ‡ and select 7:‰f(x)dx. 2. Basic Function Graphing 334 As necessary, use D and C to set the limits. Press ¸. From the Graph screen, press ‡ and select 6:Derivatives. The derivative at that ...
...Typing x values is displayed. Set the derivative point. The cursor moves to the point or type its coordinates are displayed. Finding the Numerical Integral over an Interval 1. A 4 at a Point 1. y2(x)=2xN7 Finding the Derivative (Slope) at the top of the screen marks the lower...cursor to the intersection, and its x value. 4. 5. From the Graph screen, press ‡ and select 7:‰f(x)dx. 2. Basic Function Graphing 334 As necessary, use D and C to set the limits. Press ¸. From the Graph screen, press ‡ and select 6:Derivatives. The derivative at that ...
User Manual
Page 335
... upper limit, and press ¸. Set the upper bound, and press ¸. Press ¸. The interval is shaded, and its x value. 4. From the Graph screen, press ‡ and select 8:Inflection. 2. Set the lower bound for x. Either use D and C to the lower limit or type its coordinates are displayed... Either use A and B to move the cursor to select the applicable function. 3. The cursor moves to the lower bound or type its approximate numerical integral is displayed. A 4 at the top of the screen marks the lower limit. A 4 at the top of the screen marks the lower bound. 5....
... upper limit, and press ¸. Set the upper bound, and press ¸. Press ¸. The interval is shaded, and its x value. 4. From the Graph screen, press ‡ and select 8:Inflection. 2. Set the lower bound for x. Either use D and C to the lower limit or type its coordinates are displayed... Either use A and B to move the cursor to select the applicable function. 3. The cursor moves to the lower bound or type its approximate numerical integral is displayed. A 4 at the top of the screen marks the lower limit. A 4 at the top of the screen marks the lower bound. 5....
User Manual
Page 782
...TI-89 Titanium functions and instructions in functional groups along with the page numbers where they are described. | ("with") cSolve() factor() nSolve() solve() zeros() 912 cFactor() 791 comDenom() 794 799 cZeros 803 expand() 817 819 getDenom() 825 getNum() 826 849 propFrac() 856 randPoly() 862 878 tCollect() 888 tExpand() 889 895 ‰() (integrate...898 ZoomOut 899 ZoomSqr 900 ZoomTrig 790 Circle 792 793 CyclePic 803 812 DrawParm 813 813 DrwCtour 814 822 Graph 829 835 LineTan 836 846 PtChg 856 856 ptTest() 856 857 PxlCrcl 857 857 PxlOff 858 858 PxlText 858...
...TI-89 Titanium functions and instructions in functional groups along with the page numbers where they are described. | ("with") cSolve() factor() nSolve() solve() zeros() 912 cFactor() 791 comDenom() 794 799 cZeros 803 expand() 817 819 getDenom() 825 getNum() 826 849 propFrac() 856 randPoly() 862 878 tCollect() 888 tExpand() 889 895 ‰() (integrate...898 ZoomOut 899 ZoomSqr 900 ZoomTrig 790 Circle 792 793 CyclePic 803 812 DrawParm 813 813 DrwCtour 814 822 Graph 829 835 LineTan 836 846 PtChg 856 856 ptTest() 856 857 PxlCrcl 857 857 PxlOff 858 858 PxlText 858...
User Manual
Page 788
... menu arcLen(expression1,var,start,end) ⇒ expression Returns the arc length of the current Exact/Approx mode. Regardless of the graphing mode, arc length is calculated as a decimal value, when possible, regardless of expression1 from start to end with respect to var. arcLen(cos(x),x,0,p) ¸ ...locked automatically. approx(list1) ⇒ list approx(matrix1) ⇒ matrix Returns a list or matrix where each element of expression as an integral assuming a function mode definition. arcLen(list1,var,start,end) ⇒ list Returns a list of the arc lengths of each element has ...
... menu arcLen(expression1,var,start,end) ⇒ expression Returns the arc length of the current Exact/Approx mode. Regardless of the graphing mode, arc length is calculated as a decimal value, when possible, regardless of expression1 from start to end with respect to var. arcLen(cos(x),x,0,p) ¸ ...locked automatically. approx(list1) ⇒ list approx(matrix1) ⇒ matrix Returns a list or matrix where each element of expression as an integral assuming a function mode definition. arcLen(list1,var,start,end) ⇒ list Returns a list of the arc lengths of each element has ...
User Manual
Page 832
... integer of argument 1 divided by argument 2 for each element pair. intDiv(ë 7,2) ¸ ë3 intDiv(4,5) ¸ 0 intDiv({12,ë 14,ë 16},{5,4,ë 3}) ¸ {2 ë 3 5} integrate See ‰(), page 907. The argument can be a real or a complex number. isArchiv() CATALOG isArchiv(var_name) ⇒ true,false isArchiv(PROG1) ¸ True Determines if...
... integer of argument 1 divided by argument 2 for each element pair. intDiv(ë 7,2) ¸ ë3 intDiv(4,5) ¸ 0 intDiv({12,ë 14,ë 16},{5,4,ë 3}) ¸ {2 ë 3 5} integrate See ‰(), page 907. The argument can be a real or a complex number. isArchiv() CATALOG isArchiv(var_name) ⇒ true,false isArchiv(PROG1) ¸ True Determines if...
User Manual
Page 848
not 2>=3 ¸ not x norm( ) MATH/Matrix/Norms menu norm(matrix) ⇒ expression Returns the Frobenius norm. norm([a,b;c,d]) ¸ norm([1,2;3,4]) ¸ añ +bñ +cñ +dñ 30 not MATH/Test menu not Boolean expression1 ⇒ Boolean expression Returns true, false, or a simplified Boolean expression1. Integration limits can depend on integration variables outside them. nInt(nInt(e^(ë xù y)/‡(x^2ì y^2), y,ë x,x),x,0,1) ¸ 3.304... Nest nInt() to do multiple numeric integration. Note: See also ‰().
not 2>=3 ¸ not x norm( ) MATH/Matrix/Norms menu norm(matrix) ⇒ expression Returns the Frobenius norm. norm([a,b;c,d]) ¸ norm([1,2;3,4]) ¸ añ +bñ +cñ +dñ 30 not MATH/Test menu not Boolean expression1 ⇒ Boolean expression Returns true, false, or a simplified Boolean expression1. Integration limits can depend on integration variables outside them. nInt(nInt(e^(ë xù y)/‡(x^2ì y^2), y,ë x,x),x,0,1) ¸ 3.304... Nest nInt() to do multiple numeric integration. Note: See also ‰().
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Page 907
... only upper is string2 appended to do multiple integrals. However, lower is added as C is tried first, if applicable. Such a constant might differ by a numeric constant. aò 3 xò 3 aø xò 3 + c ‰(1/(2ì cos(x)),x)! tmp(x) ¸ ClrGraph:Graph tmp(x):Graph 1/(2ì cos(x)):Graph ‡(3) (2tanê (‡(3)(tan(x/2)))/3) ¸ ‰() returns itself for pieces of...
... only upper is string2 appended to do multiple integrals. However, lower is added as C is tried first, if applicable. Such a constant might differ by a numeric constant. aò 3 xò 3 aø xò 3 + c ‰(1/(2ì cos(x)),x)! tmp(x) ¸ ClrGraph:Graph tmp(x):Graph 1/(2ì cos(x)):Graph ‡(3) (2tanê (‡(3)(tan(x/2)))/3) ¸ ‰() returns itself for pieces of...
User Manual
Page 915
... define the search interval. 180 Break The ´ key was pressed during a long calculation or during program execution. 185 Checksum error 190 Circular definition This message is displayed to ... An argument is of the wrong data type. 220 Dependent limit A limit of integration is dependent on the integration variable. Error Number Description 163 Attribute (8-digit number) of object (8-digit number)...for sending or receiving Install new batteries before sending or receiving. 170 Bound For the interactive graph math functions like 2:Zero, the lower bound must be of elements. 250 Divide by "...
... define the search interval. 180 Break The ´ key was pressed during a long calculation or during program execution. 185 Checksum error 190 Circular definition This message is displayed to ... An argument is of the wrong data type. 220 Dependent limit A limit of integration is dependent on the integration variable. Error Number Description 163 Attribute (8-digit number) of object (8-digit number)...for sending or receiving Install new batteries before sending or receiving. 170 Bound For the interactive graph math functions like 2:Zero, the lower bound must be of elements. 250 Divide by "...
User Manual
Page 945
...pp. 1-9. Algorithm Based on your x and y Window variables, the distance between xmin and xmax and between any zero crossings are calculated and plotted by xgrid and ygrid. These grid lines intersect to approximate where the zero crosses the line. • Within the ...calculated. • A sign change between ymin and ymax is divided into a number of the four corners (also called vertices or grid points) and an average value (E) is treated as found in the grid is treated similarly. Runge-Kutta Method For Runge-Kutta integrations of ordinary differential equations, the TI-89...
...pp. 1-9. Algorithm Based on your x and y Window variables, the distance between xmin and xmax and between any zero crossings are calculated and plotted by xgrid and ygrid. These grid lines intersect to approximate where the zero crosses the line. • Within the ...calculated. • A sign change between ymin and ymax is divided into a number of the four corners (also called vertices or grid points) and an average value (E) is treated as found in the grid is treated similarly. Runge-Kutta Method For Runge-Kutta integrations of ordinary differential equations, the TI-89...