User Manual
Page 80
... 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 This example illustrates using the calculus integration function. 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.
... 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 This example illustrates using the calculus integration function. 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.
User Manual
Page 242
...the APPROXIMATE setting. Otherwise, floating-point arithmetic is used after Symbolic Manipulation 242 Functions such as solve and ‰ (integrate) can use less memory than the EXACT setting. For example, you do not plan to use symbolic computations, approximate results...instead of the operands are not needed, this might be displayed as a small magnitude such as limits and integration are similar to familiar, traditional numeric calculators. Symbolic operations such as 1.23457E-11. Results with undefined variables or functions often exhibit incomplete cancellation. For ...
...the APPROXIMATE setting. Otherwise, floating-point arithmetic is used after Symbolic Manipulation 242 Functions such as solve and ‰ (integrate) can use less memory than the EXACT setting. For example, you do not plan to use symbolic computations, approximate results...instead of the operands are not needed, this might be displayed as a small magnitude such as limits and integration are similar to familiar, traditional numeric calculators. Symbolic operations such as 1.23457E-11. Results with undefined variables or functions often exhibit incomplete cancellation. For ...
User Manual
Page 243
Symbolic Manipulation 243 Similarly, ä (integrate) uses approximate numerical methods if appropriate where exact symbolic methods fail. Advantages Disadvantages You see exact results when practical, and approximate numeric results when exact ...
Symbolic Manipulation 243 Similarly, ä (integrate) uses approximate numerical methods if appropriate where exact symbolic methods fail. Advantages Disadvantages You see exact results when practical, and approximate numeric results when exact ...
User Manual
Page 266
... Manipulation 266 Evaluates an expression at discrete variable values within a range and then calculates the sum. Finds candidate values of an expression with respect to a specified variable. Calculates a Taylor polynomial approximation to an expression with or without initial conditions. Calculates an integral as a floating-point number using quadrature (an approximation using weighted sums of...
... Manipulation 266 Evaluates an expression at discrete variable values within a range and then calculates the sum. Finds candidate values of an expression with respect to a specified variable. Calculates a Taylor polynomial approximation to an expression with or without initial conditions. Calculates an integral as a floating-point number using quadrature (an approximation using weighted sums of...
User Manual
Page 267
...is not the same as typing the letter D on the keyboard. Calc toolbar menu. To get d, use ... 1 or 2 =. Symbolic Manipulation 267 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 ... =. It is a special symbol. For complete information about any calculus function, refer to x. Note: The d symbol for some of integration d (expression, var [,order]) Integrate x2†sin(x) with respect to the Technical Reference module.
...is not the same as typing the letter D on the keyboard. Calc toolbar menu. To get d, use ... 1 or 2 =. Symbolic Manipulation 267 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 ... =. It is a special symbol. For complete information about any calculus function, refer to x. Note: The d symbol for some of integration d (expression, var [,order]) Integrate x2†sin(x) with respect to the Technical Reference module.
User Manual
Page 268
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. Note: You can integrate an expression only; Note: You can find a limit for an expression, list, or matrix. Symbolic Manipulation 268 Finding a Limit Use the limit (... 3) function. 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. Note: You can integrate an expression only; Note: You can find a limit for an expression, list, or matrix. Symbolic Manipulation 268 Finding a Limit Use the limit (... 3) function. you can differentiate an expression, list, or matrix.
User Manual
Page 272
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. 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
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). Then integrate y1(x) with respect to x. Use the TI-89 Titanium's built-in when function.
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). Then integrate y1(x) with respect to x. Use the TI-89 Titanium's built-in when function.
User Manual
Page 331
... of two functions. Finds the intersection of the Math Menu Press ‡ from the Graph screen. Draws and measures a line between two points along a curve. Basic Function Graphing 331 Math Tool Value Zero, Minimum, Maximum Intersection Derivatives ‰f(x)dx Inflection Distance Tangent Arc... the derivative (slope) at a point. Finds the approximate numerical integral over an interval. On the Derivatives submenu, only dy/dx is available for other derivatives are available for function graphing. The other graphing modes (parametric, polar, etc.). Finds the arc length between two...
... of two functions. Finds the intersection of the Math Menu Press ‡ from the Graph screen. Draws and measures a line between two points along a curve. Basic Function Graphing 331 Math Tool Value Zero, Minimum, Maximum Intersection Derivatives ‰f(x)dx Inflection Distance Tangent Arc... the derivative (slope) at a point. Finds the approximate numerical integral over an interval. On the Derivatives submenu, only dy/dx is available for other derivatives are available for function graphing. The other graphing modes (parametric, polar, etc.). Finds the arc length between two...
User Manual
Page 332
...and qc if you press A or B, the free-moving cursor appears. The cursor moves to that x value on the number of functions graphed. • If only one function is displayed. You may not be able to move it back to move the cursor between any two ...functions within an interval. Derivatives, integrals, distances, etc., are graphed, this shades the area between functions at a Specified Point 1. Basic Function Graphing 332 From the Graph screen, press ‡ and select 1:Value. 2. Type the x value, which must be an...
...and qc if you press A or B, the free-moving cursor appears. The cursor moves to that x value on the number of functions graphed. • If only one function is displayed. You may not be able to move it back to move the cursor between any two ...functions within an interval. Derivatives, integrals, distances, etc., are graphed, this shades the area between functions at a Specified Point 1. Basic Function Graphing 332 From the Graph screen, press ‡ and select 1:Value. 2. Type the x value, which must be an...
User Manual
Page 334
...select 1:dy/dx from the submenu. 2. The derivative at a Point 1. From the Graph screen, press ‡ and select 7:‰f(x)dx. 2. As necessary, use D and C to select the applicable function. 3. Basic Function Graphing 334 The cursor moves to the intersection, and its x value. 4. Press ¸...Slope) at that point is a quick way to the point or type its coordinates are displayed. From the Graph screen, press ‡ and select 6:Derivatives. Finding the Numerical Integral over an Interval 1. 5. Press ¸. A 4 at the top of the screen marks the lower bound....
...select 1:dy/dx from the submenu. 2. The derivative at a Point 1. From the Graph screen, press ‡ and select 7:‰f(x)dx. 2. As necessary, use D and C to select the applicable function. 3. Basic Function Graphing 334 The cursor moves to the intersection, and its x value. 4. Press ¸...Slope) at that point is a quick way to the point or type its coordinates are displayed. From the Graph screen, press ‡ and select 6:Derivatives. Finding the Numerical Integral over an Interval 1. 5. Press ¸. A 4 at the top of the screen marks the lower bound....
User Manual
Page 335
...the cursor to the lower bound or type its x value. 4. Press ¸. Finding an Inflection Point within the interval, and its approximate numerical integral is shaded, and its coordinates are displayed. Set the lower bound for x. A 4 at the top of the screen marks the lower limit.... Set the upper limit, and press ¸. The interval is displayed. Basic Function Graphing 335 As necessary, use D and C to the inflection point (if any) within an Interval 1. Press ¸. From the Graph screen, press ‡ and select 9:Distance. A 4 at the top of the ...
...the cursor to the lower bound or type its x value. 4. Press ¸. Finding an Inflection Point within the interval, and its approximate numerical integral is shaded, and its coordinates are displayed. Set the lower bound for x. A 4 at the top of the screen marks the lower limit.... Set the upper limit, and press ¸. The interval is displayed. Basic Function Graphing 335 As necessary, use D and C to the inflection point (if any) within an Interval 1. Press ¸. From the Graph screen, press ‡ and select 9:Distance. A 4 at the top of the ...
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
...; 15!arctest ¸ Done 50 You can access an archived variable the same as an integral assuming a function mode definition. Regardless of expression1 from the Home screen 1 ¸ 1 ... Returns a previous answer from start ,end) ⇒ expression Returns the arc length of the graphing mode, arc length is from RAM to var. arcLen(cos(x),x,0,p) ¸ 3.820... N Unarchiv...current Exact/Approx mode. However, you would a variable in RAM. Valid range for integer is calculated as you cannot delete, rename, or store to 99 and cannot be an expression. arcLen(f(x),x,a,b)...
...; 15!arctest ¸ Done 50 You can access an archived variable the same as an integral assuming a function mode definition. Regardless of expression1 from the Home screen 1 ¸ 1 ... Returns a previous answer from start ,end) ⇒ expression Returns the arc length of the graphing mode, arc length is from RAM to var. arcLen(cos(x),x,0,p) ¸ 3.820... N Unarchiv...current Exact/Approx mode. However, you would a variable in RAM. Valid range for integer is calculated as you cannot delete, rename, or store to 99 and cannot be an expression. arcLen(f(x),x,a,b)...
User Manual
Page 832
... OFF. start is > the length of argument 1 divided by argument 2. 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. Returns false if the clock is archived. If srcString does not contain subString...
... OFF. start is > the length of argument 1 divided by argument 2. 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. Returns false if the clock is archived. If srcString does not contain subString...
User Manual
Page 848
not 2>=3 ¸ not x norm( ) MATH/Matrix/Norms menu norm(matrix) ⇒ expression Returns the Frobenius norm. Nest nInt() to do multiple numeric integration. nInt(nInt(e^(ë xù y)/‡(x^2ì y^2), y,ë x,x),x,0,1) ¸ 3.304... Note: See also ‰(). Integration limits can depend on integration variables outside them. 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.
not 2>=3 ¸ not x norm( ) MATH/Matrix/Norms menu norm(matrix) ⇒ expression Returns the Frobenius norm. Nest nInt() to do multiple numeric integration. nInt(nInt(e^(ë xù y)/‡(x^2ì y^2), y,ë x,x),x,0,1) ¸ 3.304... Note: See also ‰(). Integration limits can depend on integration variables outside them. 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.
User Manual
Page 907
...those places. Moreover, piecewise constant expressions are omitted. For the AUTO setting of the Exact/Approx mode, numerical integration is made to string1. ‰ ( ) (integrate) 2 < key ‰(expression1, var[, lower] [,upper]) ⇒ expression ‰(list1,var [,order]) ... ¸ Appendix A: Functions and Instructions 907 Such a constant might differ by a numeric constant. tmp(x) ¸ ClrGraph:Graph tmp(x):Graph 1/(2ì cos(x)):Graph ‡(3) (2tanê (‡(3)(tan(x/2)))/3) ¸ ‰() returns itself for pieces of expression1 with respect to the variable...
...those places. Moreover, piecewise constant expressions are omitted. For the AUTO setting of the Exact/Approx mode, numerical integration is made to string1. ‰ ( ) (integrate) 2 < key ‰(expression1, var[, lower] [,upper]) ⇒ expression ‰(list1,var [,order]) ... ¸ Appendix A: Functions and Instructions 907 Such a constant might differ by a numeric constant. tmp(x) ¸ ClrGraph:Graph tmp(x):Graph 1/(2ì cos(x)):Graph ‡(3) (2tanê (‡(3)(tan(x/2)))/3) ¸ ‰() returns itself for pieces of expression1 with respect to the variable...
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Page 915
... than the upper bound to define the search interval. 180 Break The ´ key was pressed during a long calculation or during simplification. Error Number Description 163 Attribute (8-digit number) of object (8-digit number) not found 165 Batteries too...because the argument 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 used to avoid running out of memory during infinite... argument is of the wrong data type. 220 Dependent limit A limit of integration is dependent on the...
... than the upper bound to define the search interval. 180 Break The ´ key was pressed during a long calculation or during simplification. Error Number Description 163 Attribute (8-digit number) of object (8-digit number) not found 165 Batteries too...because the argument 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 used to avoid running out of memory during infinite... argument is of the wrong data type. 220 Dependent limit A limit of integration is dependent on the...
User Manual
Page 945
...integrations of ordinary differential equations, the TI-89 Titanium / Voyage™ 200 uses the Bogacki-Shampine 3(2) formula as the value of the equation at each of the five points shown to the right, the difference between the point's z value and the contour value is calculated...interpolation is used to form a series of the four corners (also called vertices or grid points) and an average value (E) is calculated: E = z---1-----+-----z--2-----+4-----z--3-----+-----z--4-- These grid lines intersect to approximate where the zero crosses the line. • Within the rectangle, any two ...
...integrations of ordinary differential equations, the TI-89 Titanium / Voyage™ 200 uses the Bogacki-Shampine 3(2) formula as the value of the equation at each of the five points shown to the right, the difference between the point's z value and the contour value is calculated...interpolation is used to form a series of the four corners (also called vertices or grid points) and an average value (E) is calculated: E = z---1-----+-----z--2-----+4-----z--3-----+-----z--4-- These grid lines intersect to approximate where the zero crosses the line. • Within the rectangle, any two ...