Texas Instruments TI-89 user guide: = (equal) □ key

= (equal) □ key

expression1 = expression2 ⇒ Boolean expression
list1 = list2 ⇒ Boolean list
matrix1 = matrix2 ⇒ Boolean matrix

Returns true if expression1 is determined to be equal to expression2.

Returns false if expression1 is determined to not be equal to expression2.

Anything else returns a simplified form of the equation.

For lists and matrices, returns comparisons element by element.

Example function listing using math test symbols: =, ≠, <, ≤, >, ≥

:g(x) :Func :If x≤-5 Then : Return 5 : ElseIf x>-5 and x<0 Then : Return -x : ElseIf x≥0 and x≠10 Then : Return x : ElseIf x=10 Then : Return 3 :EndIf :EndFunc

Graph g(x) ENTER

≠ □ □ key

expression1 ≠ expression2 ⇒ Boolean expression
list1 ≠ list2 ⇒ Boolean list
matrix1 ≠ matrix2 ⇒ Boolean matrix

Returns true if expression1 is determined to be not equal to expression2.

Returns false if expression1 is determined to be equal to expression2.

Anything else returns a simplified form of the equation.

For lists and matrices, returns comparisons element by element.

See "=" (equal) example.

< [2nd] [<] key

expression1 < expression2 ⇒ Boolean expression
list1 < list2 ⇒ Boolean list
matrix1 < matrix2 ⇒ Boolean matrix

Returns true if expression1 is determined to be less than expression2.

Returns false if expression1 is determined to be greater than or equal to expression2.

Anything else returns a simplified form of the equation.

For lists and matrices, returns comparisons element by element.

See "=" (equal) example.

Appendix A: Functions and Instructions 529

≤

□0 key

expression1 ≤ expression2 ⇒ Boolean expression See "=" (equal) example. list1 ≤ list2 ⇒ Boolean list matrix1 ≤ matrix2 ⇒ Boolean matrix

Returns true if expression1 is determined to be less than or equal to expression2.

Returns false if expression1 is determined to be greater than expression2.

Anything else returns a simplified form of the equation.

For lists and matrices, returns comparisons element by element.

2nd [>] key

expression1 > expression2 ⇒ Boolean expression See "=" (equal) example. list1 > list2 ⇒ Boolean list matrix1 > matrix2 ⇒ Boolean matrix

Returns true if expression1 is determined to be greater than expression2.

Returns false if expression1 is determined to be less than or equal to expression2.

Anything else returns a simplified form of the equation.

For lists and matrices, returns comparisons element by element.

≥

□. key

expression1 ≥ expression2 ⇒ Boolean expression See "=" (equal) example. list1 ≥ list2 ⇒ Boolean list matrix1 ≥ matrix2 ⇒ Boolean matrix

Returns true if expression1 is determined to be greater than or equal to expression2.

Returns false if expression1 is determined to be less than expression2.

Anything else returns a simplified form of the equation.

For lists and matrices, returns comparisons element by element.

.+ (dot add) □+ keys

matrix1 .+ matrix2 ⇒ matrix [a,2;b,3].+[c,4;5,d] ENTER expression .+ matrix1 ⇒ matrix x.+[c,4;5,d] ENTER

matrix1 .+ matrix2 returns a matrix that is the sum of each pair of corresponding elements in matrix1 and matrix2.

expression .+ matrix1 returns a matrix that is the sum of expression and each element in matrix1.

530 Appendix A: Functions and Instructions

.- (dot subt.) □ □ keys

matrix1 .- matrix2 ⇒ matrix
expression .- matrix1 ⇒ matrix

matrix1 .- matrix2 returns a matrix that is the difference between each pair of corresponding elements in matrix1 and matrix2.

expression .- matrix1 returns a matrix that is the difference of expression and each element in matrix1.

[ a,2;b,3 ] .- [ c,4;d,5 ] ENTER x .- [ c,4;d,5 ] ENTER

.* (dot mult.) □ × keys

matrix1 .* matrix2 ⇒ matrix
expression .* matrix1 ⇒ matrix

matrix1 .* matrix2 returns a matrix that is the product of each pair of corresponding elements in matrix1 and matrix2.

expression .* matrix1 returns a matrix containing the products of expression and each element in matrix1.

[ a,2;b,3 ] .* [ c,4;5,d ] ENTER x .* [ a,b;c,d ] ENTER

./ (dot divide) □ ÷ keys

matrix1 ./ matrix2 ⇒ matrix
expression ./ matrix1 ⇒ matrix

matrix1 ./ matrix2 returns a matrix that is the quotient of each pair of corresponding elements in matrix1 and matrix2.

expression ./ matrix1 returns a matrix that is the quotient of expression and each element in matrix1.

[ a,2;b,3 ] ./ [ c,4;5,d ] ENTER x ./ [ c,4;5,d ] ENTER

.^ (dot power) □ ^ keys

matrix1 .^ matrix2 ⇒ matrix
expression .^ matrix1 ⇒ matrix

matrix1 .^ matrix2 returns a matrix where each element in matrix2 is the exponent for the corresponding element in matrix1.

expression .^ matrix1 returns a matrix where each element in matrix1 is the exponent for expression.

[ a,2;b,3 ] .^ [ c,4;5,d ] ENTER x .^ [ c,4;5,d ] ENTER

! (factorial) TI-89: □ ÷ key TI-92 Plus: 2nd W key

expression! ⇒ expression
list! ⇒ list
matrix! ⇒ matrix

Returns the factorial of the argument.

For a list or matrix, returns a list or matrix of factorials of the elements.

The TI-89 computes a numeric value for only non-negative whole-number values.

5! ENTER 120 {5,4,3}! ENTER {120 24 6} [1,2;3,4]! ENTER [1 2] [6 24]

Appendix A: Functions and Instructions 531

& (append) TI-89: \diamondsuit × key TI-92 Plus: 2nd H key

string1 & string2 \Rightarrow string "Hello " & "Nick" ENTER "Hello Nick"

Returns a text string that is string2 appended to string1.

\int() (integrate) 2nd [\int] key

\int(expression1, var[, lower] [,upper]) \Rightarrow expression \int(list1,var [,order]) \Rightarrow list \int(matrix1,var [,order]) \Rightarrow matrix

Returns the integral of expression1 with respect to the variable var from lower to upper. \int(x^2,x,a,b) ENTER b^3/3 - a^3/3

Returns an anti-derivative if lower and upper are omitted. A symbolic constant of integration such as C is omitted. \int(x^2,x) ENTER x^3/3

However, lower is added as a constant of integration if only upper is omitted. \int(a* x^2,x,c) ENTER a \cdot x^3/3 + c

Equally valid anti-derivatives might differ by a numeric constant. Such a constant might be disguised—particularly when an anti-derivative contains logarithms or inverse trigonometric functions. Moreover, piecewise constant expressions are sometimes added to make an anti-derivative valid over a larger interval than the usual formula. \int(1/(2-cos(x)),x)\rightarrowtmp(x) ENTER ClrGraph:Graph tmp(x):Graph 1/(2-cos(x)):Graph \sqrt(3) (2tan$^{-1}$(\sqrt(3)(tan(x/2)))/3) ENTER \int (1/2-\cos(x)) dx \quad 1/2-\cos(x) \frac2\sqrt3 \cdot \tan^-1(\sqrt3 \cdot \tan(x/2))

\int() returns itself for pieces of expression1 that it cannot determine as an explicit finite combination of its built-in functions and operators. When lower and upper are both present, an attempt is made to locate any discontinuities or discontinuous derivatives in the interval lower < var < upper and to subdivide the interval at those places. For the AUTO setting of the Exact/Approx mode, numerical integration is used where applicable when an anti-derivative or a limit cannot be determined. For the APPROX setting, numerical integration is tried first, if applicable. Anti-derivatives are sought only where such numerical integration is inapplicable or fails. \int(b* e^(-x^2)+a/(x^2+a^2),x) ENTER

\blacksquare \int (b \cdot e^-x^2 + a/x^2+a^2) dx b \int (e^-x^2) dx + \tan^-1(x/a) \int(e^(-x^2),x,-1,1)\diamondsuit ENTER 1.493...

532 Appendix A: Functions and Instructions

∫() can be nested to do multiple integrals. Integration limits can depend on integration variables outside them.

Note: See also nInt().

∫(∫(ln(x+y),y,0,x),x,0,a) [ENTER]

∫₀ᵃ ∫₀ˣ ln(x+y) dy dx a²·ln(a)/2 + a²·(ln(2) - □/□)

√() (square root) [2nd] [√] key

√(expression1) ⇒ expression √(list1) ⇒ list

Returns the square root of the argument.

For a list, returns the square roots of all the elements in list1.

√(4) [ENTER] 2 √({9,a,4}) [ENTER] {3 √a 2}

Π() (product) MATH/Calculus menu

Π(expression1, var, low, high) ⇒ expression

Evaluates expression1 for each value of var from low to high, and returns the product of the results.

Π(1/n,n,1,5) [ENTER] 1/120 Π(k^2,k,1,n) [ENTER] (n!)² Π({1/n,n,2},n,1,5) [ENTER] {1/120 120 32}

Π(expression1, var, low, low−1) ⇒ 1

Π(k,k,4,3) [ENTER] 1

Π(expression1, var, low, high) ⇒ 1/Π(expression1, var, high+1, low−1) if high < low−1

Π(1/k,k,4,1) [ENTER] 6 Π(1/k,k,4,1)*Π(1/k,k,2,4) [ENTER] 1/4

Σ() (sum) MATH/Calculus menu

Σ(expression1, var, low, high) ⇒ expression

Evaluates expression1 for each value of var from low to high, and returns the sum of the results.

Σ(1/n,n,1,5) [ENTER] 137/60 Σ(k^2,k,1,n) [ENTER] n·(n+1)·(2·n+1)/6

Σ(1/n^2,n,1,∞) [ENTER] π²/6 Σ(k,k,4,3) [ENTER] 0

Σ(expression1, var, low, low−1) ⇒ 0

Σ(expression1, var, low, high) ⇒ −Σ(expression1, var, high+1, low−1) if high < low−1

Σ(k,k,4,1) [ENTER] −5 Σ(k,k,4,1)+Σ(k,k,2,4) [ENTER] 4

Appendix A: Functions and Instructions 533

\wedge (power) key

expression1 ^ expression2 \Rightarrow expression list1 ^ list2 \Rightarrow list

Returns the first argument raised to the power of the second argument.

For a list, returns the elements in list1 raised to the power of the corresponding elements in list2.

In the real domain, fractional powers that have reduced exponents with odd denominators use the real branch versus the principal branch for complex mode.

4^2 [ENTER] 16 {a,2,c}^{1,b,3} [ENTER] {a $2^b$ c$^3$}

expression ^ list1 \Rightarrow list

Returns expression raised to the power of the elements in list1.

p^{a,2,-3} [ENTER] {p$^a$ p$^2$ 1/p^3}

list1 ^ expression \Rightarrow list

Returns the elements in list1 raised to the power of expression.

{1,2,3,4}^-2 [ENTER] {1 1/4 1/9 1/16}

squareMatrix1 ^ integer \Rightarrow matrix

Returns squareMatrix1 raised to the integer power.

squareMatrix1 must be a square matrix.

If integer = -1, computes the inverse matrix. If integer < -1, computes the inverse matrix to an appropriate positive power.

[1,2;3,4]^2 [ENTER] [1,2;3,4]^-1 [ENTER] [1,2;3,4]^-2 [ENTER]

# (indirection) CATALOG

varNameString

Refers to the variable whose name is varNameString. This lets you create and modify variables from a program using strings.

Program segment:

\vdots :Request "Enter Your Name",str1 :NewFold #str1 \vdots \vdots :For i,1,5,1 : ClrGraph : Graph i*x : StoPic #("pic" & string(i)) :EndFor \vdots

534 Appendix A: Functions and Instructions

(radian) MATH/Angle menu

expression1^r \Rightarrow expression list1^r \Rightarrow list matrix1^r \Rightarrow matrix

In Degree angle mode, multiplies expression1 by 180/\pi. In Radian angle mode, returns expression1 unchanged.

This function gives you a way to use a radian angle while in Degree mode. (In Degree angle mode, sin(), cos(), tan(), and polar-to-rectangular conversions expect the angle argument to be in degrees.)

Hint: Use $^r$ if you want to force radians in a function or program definition regardless of the mode that prevails when the function or program is used.

In Degree or Radian angle mode:

\cos((\pi/4)^r) [ENTER] \frac\sqrt22

\cos(\0^r, (\pi/12)^r, -\pi^r) [ENTER]

\1 \quad \frac(\sqrt3+1)\cdot\sqrt24 \quad -1\

(degree) 2nd [°] key

expression° \Rightarrow value list1° \Rightarrow list matrix1° \Rightarrow matrix

In Radian angle mode, multiplies expression by \pi/180. In Degree angle mode, returns expression unchanged.

This function gives you a way to use a degree angle while in Radian mode. (In Radian angle mode, sin(), cos(), tan(), and polar-to-rectangular conversions expect the angle argument to be in radians.)

In Radian angle mode:

\cos(45°) [ENTER] \frac\sqrt22

\cos(\0, \pi/4, 90°, 30.12°) [D] [ENTER] {1 .707... 0 .864...}

(angle) 2nd [\angle] key

[radius,\angle\theta_angle] \Rightarrow vector (polar input) [radius,\angle\theta_angle,Z_coordinate] \Rightarrow vector (cylindrical input) [radius,\angle\theta_angle,\angle\phi_angle] \Rightarrow vector (spherical input)

Returns coordinates as a vector depending on the Vector Format mode setting: rectangular, cylindrical, or spherical.

[5,\angle60°,\angle45°] [ENTER]

In Radian mode and vector format set to:

[magnitude \angle angle] \Rightarrow complexValue (polar input)

Enters a complex value in (r\angle\theta) polar form. The angle is interpreted according to the current Angle mode setting.

In Radian angle mode and Rectangular complex format mode:

5+3i-(10\angle\pi/4) [ENTER]

5-5\cdot\sqrt2+(3-5\cdot\sqrt2)\cdot i

[D] [ENTER] -2.071...-4.071...\cdot i

Appendix A: Functions and Instructions 535

°, ', "

[2nd] [°] key (°), [2nd] ['] key ('), [2nd] ["] key (")

dd°mm'ss.ss" ⇒ expression

dd A positive or negative number
mm A non-negative number
ss.ss A non-negative number

Returns dd+(mm/60)+(ss.ss/3600).

This base-60 entry format lets you:

• Enter an angle in degrees/minutes/seconds without regard to the current angle mode.
• Enter time as hours/minutes/seconds.

In Degree angle mode:

25°13'17.5" [ENTER] 25.221...
25°30' [ENTER] 51/2

' (prime) [2nd] ['] key

variable'
variable''

Enters a prime symbol in a differential equation. A single prime symbol denotes a 1st-order differential equation, two prime symbols denote a 2nd-order, etc.

deSolve(y''=y^(-1/2) and y(0)=0 and y'(0)=0,t,y) [ENTER]

\frac2 \cdot y^3/43 = t

_ (underscore) TI-89: [♦] [] key TI-92 Plus: [2nd] [] key

expression_unit

Designates the units for an expression. All unit names must begin with an underscore.

You can use pre-defined units or create your own units. For a list of pre-defined units, refer to the chapter about constants and measurement units in this book. You can press:

TI-89: [2nd] [UNITS]
TI-92 Plus: [♦] [UNITS]

to select units from a menu, or you can type the unit names directly.

3_m►_ft [ENTER] 9.842...·_ft

Note: To type ►, press [2nd] [►].

variable_

When variable has no value, it is treated as though it represents a complex number. By default, without the _, the variable is treated as real.

If variable has a value, the _ is ignored and variable retains its original data type.

Note: You can store a complex number to a variable without using _. However, for best results in calculations such as cSolve() and cZeros(), the _ is recommended.

Assuming z is undefined:

real(z) [ENTER] z
real(z_) [ENTER] real(z_)
imag(z) [ENTER] 0
imag(z_) [ENTER] imag(z_)

536 Appendix A: Functions and Instructions

(convert) 2nd [►] key

expression_unit1 unit2 \Rightarrow expression_unit2 3_m ft ENTER 9.842..._ft

Converts an expression from one unit to another. The units must be in the same category.

The _ underscore character designates the units. For a list of valid pre-defined units, refer to the chapter about constants and measurement units in this book. You can press: TI-89: 2nd [UNITS] TI-92 Plus: [◆][UNITS] to select units from a menu, or you can type the unit names directly.

To get the _ underscore when typing units directly, press: TI-89: [] TI-92 Plus: 2nd []

Note: The \blacktriangleright conversion operator does not handle temperature units. Use tmpCnv() and AtmpCnv() instead.

10^() CATALOG

10^(expression1) \Rightarrow expression 10^(list1) \Rightarrow list 10^(1.5) ENTER 31.622... 10^{0,-2,2,a} ENTER {1 1/100 100 $10^a$}

Returns 10 raised to the power of the argument.

For a list, returns 10 raised to the power of the elements in list1.

10^(squareMatrix1) \Rightarrow squareMatrix 10^([1,5,3;4,2,1;6,-2,1]) ENTER Returns 10 raised to the power of squareMatrix1. This is not the same as calculating 10 raised to the power of each element. For information about the calculation method, refer to cos().

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

Appendix A: Functions and Instructions 537

x⁻¹

CATALOG (^-1)

expression1 x⁻¹ \Rightarrow expression list1 x⁻¹ \Rightarrow list

Returns the reciprocal of the argument. For a list, returns the reciprocals of the elements in list1.

3.1^-1 [ENTER] .322581 {a,4,-.1,x-2}^-1 [ENTER] {1/a 1/4 -10. 1/(x-2)}

squareMatrix1 x⁻¹ \Rightarrow squareMatrix

Returns the inverse of squareMatrix1. squareMatrix1 must be a non-singular square matrix.

[1,2;3,4]^-1 [ENTER] [1,2;a,4]^-1 [ENTER]

\begin{tabular}{ll} \beginbmatrix 1 & 2 \ 3 & 4 \endbmatrix^-1 & \beginbmatrix -2 & 1 \ 3/2 & -1/2 \endbmatrix \ \beginbmatrix 1 & 2 \ a & 4 \endbmatrix^-1 & \beginbmatrix -2/a-2 & 1/a-2 \ a/2(a-2) & -1/2(a-2) \endbmatrix \ \end{tabular}

| ("with") TI-89: [1] key TI-92 Plus: [2nd] [1] key

expression | Boolean expression1 [and Boolean expression2]...[and Boolean expressionN]

The "with" (|) symbol serves as a binary operator. The operand to the left of | is an expression. The operand to the right of | specifies one or more relations that are intended to affect the simplification of the expression. Multiple relations after | must be joined by a logical "and".

The "with" operator provides three basic types of functionality: substitutions, interval constraints, and exclusions.

Substitutions are in the form of an equality, such as x=3 or y=sin(x). To be most effective, the left side should be a simple variable. expression | variable = value will substitute value for every occurrence of variable in expression.

Interval constraints take the form of one or more inequalities joined by logical "and" operators. Interval constraints also permit simplification that otherwise might be invalid or not computable.

Exclusions use the "not equals" (/= or \neq) relational operator to exclude a specific value from consideration. They are used primarily to exclude an exact solution when using cSolve(), cZeros(), fMax(), fMin(), solve(), zeros(), etc.

x+1 | x=3 [ENTER] 4 x+y | x=sin(y) [ENTER] sin(y)+y x+y | sin(y)=x [ENTER] x+y

x^3-2x+7\rightarrowf(x) [ENTER] Done f(x) | x=\sqrt3 [ENTER] \sqrt3+7

(sin(x))^2+2sin(x)-6 | sin(x)=d [ENTER] d²+2d-6

solve(x^2-1=0,x)|x>0 and x<2 [ENTER] x=1

\sqrtx*\sqrt(1/x) | x>0 [ENTER] 1

\sqrtx*\sqrt(1/x) [ENTER] \sqrt1/x \cdot \sqrtx

solve(x^2-1=0,x) | x\neq1 [ENTER] x=-1

538 Appendix A: Functions and Instructions

\rightarrow (store) \quad [STO\rceil] key

expression \rightarrow var list \rightarrow var matrix \rightarrow var expression \rightarrow fun_name(parameter1,...) list \rightarrow fun_name(parameter1,...) matrix \rightarrow fun_name(parameter1,...)

\pi/4 \rightarrow myvar [ENTER] \qquad \pi/4 2cos(x) \rightarrow Y1(x) [ENTER] \qquad Done {1,2,3,4} \rightarrow Lst5 [ENTER] \qquad {1 2 3 4} [1,2,3:4,5,6] \rightarrow MatG [ENTER] \qquad \beginbmatrix 1 & 2 & 3 \ 4 & 5 & 6 \endbmatrix "Hello" \rightarrow str1 [ENTER] \qquad "Hello"

If variable var does not exist, creates var and initializes it to expression, list, or matrix.

If var already exists and if it is not locked or protected, replaces its contents with expression, list, or matrix.

Hint: If you plan to do symbolic computations using undefined variables, avoid storing anything into commonly used, one-letter variables such as a, b, c, x, y, z, etc.

\bullet (comment) Program Editor/Control menu or TI-89: [\blacklozenge] [ ] key TI-92 Plus: [2nd] X key

\bullet [text]

\bullet processes text as a comment line, which can be used to annotate program instructions.

\bullet can be at the beginning or anywhere in the line. Everything to the right of \bullet, to the end of the line, is the comment.

Program segment: : :• Get 10 points from the Graph screen :For i,1,10 • This loops 10 times :

0b, 0h TI-89: [0] [alpha] [B] keys TI-92 Plus: [0] B keys TI-89: [0] [alpha] [H] keys TI-92 Plus: [0] H keys

0binaryNumber 0hexadecimalNumber

Denotes a binary or hexadecimal number, respectively. To enter a binary or hex number, you must enter the 0b or 0h prefix regardless of the Base mode. Without a prefix, a number is treated as decimal (base 10).

Results are displayed according to the Base mode.

In Dec base mode: 0b10+0hF+10 [ENTER] \qquad 27

In Bin base mode: 0b10+0hF+10 [ENTER] \qquad 0b11011

In Hex base mode: 0b10+0hF+10 [ENTER] \qquad 0h1B

Appendix A: Functions and Instructions 539

540 Appendix A: Functions and Instructions

Reference Information

B

• TI-89 / TI-92 Plus Error Messages ........ 542
• Modes ........ 550
• TI-89 / TI-92 Plus Character Codes ........ 555
• TI-89 Key Codes ........ 556
• TI-92 Plus Key Codes ........ 559
• Entering Complex Numbers ........ 563
• Accuracy Information ........ 566
• System Variables and Reserved Names ........ 567
• EOS (Equation Operating System) Hierarchy ........ 568
• Regression Formulas ........ 570
• Contour Levels and Implicit Plot Algorithm ........ 572
• Runge-Kutta Method ........ 573

This appendix contains a comprehensive list of TI-89 / TI-92 Plus error messages and character codes. It also includes information about how certain TI-89 / TI-92 Plus operations are calculated.

For additional information, refer to Appendix C. For example, if you have difficulty operating the TI-89 / TI-92 Plus, Appendix C contains an “In Case of Difficulty” section that gives suggestions that may help you correct the problem.

Appendix B: Reference Information 541

TI-89 / TI-92 Plus Error Messages

This section lists error messages that may be displayed when input or internal errors are encountered. The number to the left of each error message represents an internal error number that is not displayed. If the error occurs inside a Try...EndTry block, the error number is stored in system variable erronum. Many of the error messages are self-explanatory and do not require descriptive information. However, additional information has been added for some error messages.

542 Appendix B: Reference Information

Error Number Description

160 Argument must be an expression For example, zeros(2x+3=0,x) is invalid because the first argument is an equation.

161 ASAP or Exec string too long

163 Attribute (8-digit number) of object (8-digit number) not found

165 Batteries too low for sending/receiving product code Install new batteries before sending or receiving product software (base code).

170 Bound For the interactive graph math functions like 2:Zero, the lower bound must be less than the upper bound to define the search interval.

180 Break The ON key was pressed during a long calculation or during program execution.

185 Checksum error

190 Circular definition This message is displayed to avoid running out of memory during infinite replacement of variable values during simplification. For example, a+1►a, where a is an undefined variable, will cause this error.

200 Constraint expression invalid For example, solve(3x^2- 4=0, x) | x<0 or x>5 would produce this error message because the constraint is separated by “or” and not “and.”

210 Data type An argument is of the wrong data type.

220 Dependent limit A limit of integration is dependent on the integration variable. For example, ∫(x^2,x,1,x) is not allowed.

225 Diff Eq setup

230 Dimension A list or matrix index is not valid. For example, if the list {1,2,3,4} is stored in L1, then L1[5] is a dimension error because L1 only contains four elements.

240 Dimension mismatch Two or more arguments must be of the same dimension. For example, [1,2]+[1,2,3] is a dimension mismatch because the matrices contain a different number of elements.

250 Divide by zero

Appendix B: Reference Information 543

Error Number Description

260 Domain error An argument must be in a specified domain. For example, ans(100) is not valid because the argument for ans() must be in the range 1–99.

270 Duplicate variable name

280 Else and ElseIf invalid outside of If..EndIf block

290 EndTry is missing the matching Else statement

295 Excessive iteration

300 Expected 2 or 3-element list or matrix

307 Flash application extension (function or program) not found

308 Flash application not found

310 First argument of nSolve must be a univariate equation The first argument must be an equation, and the equation cannot contain a non-valued variable other than the variable of interest. For example, nSolve(3x^2- 4=0, x) is a valid equation; however, nSolve(3x^2- 4, x) is not an equation, and nSolve(3x^2- y=0,x) is not a univariate equation because y has no value in this example.

320 First argument of solve or cSolve must be an equation or inequality For example, solve(3x^2- 4, x) is invalid because the first argument is not an equation.

330 Folder An attempt was made in the VAR-LINK menu to store a variable in a folder that does not exist.

335 Graph functions y1(x)...y99(x) not available in Diff Equations mode

345 Inconsistent units

350 Index out of range

360 Indirection string is not a valid variable name

380 Invalid ans()

390 Invalid assignment

400 Invalid assignment value

544 Appendix B: Reference Information

Error Number Description

405 Invalid axes 410 Invalid command 420 Invalid folder name 430 Invalid for the current mode settings 440 Invalid implied multiply For example, x(x+1) is invalid; whereas, x* (x+1) is the correct syntax. This is to avoid confusion between implied multiplication and function calls. 450 Invalid in a function or current expression Only certain commands are valid in a user-defined function. Entries that are made in the Window Editor, Table Editor, Data/Matrix Editor, and Solver as well as system prompts such as Lower Bound cannot contain any commands or a colon (:). See also “Creating and Evaluating User-Defined Functions” in Chapter 5. 460 Invalid in Custom..EndCustm block 470 Invalid in Dialog..EndDlog block 480 Invalid in Toolbar..EndTBar block 490 Invalid in Try..EndTry block 500 Invalid label Label names must follow the same rules used for naming variables. 510 Invalid list or matrix For example, a list inside a list such as {2,{3,4}} is not valid. 520 Invalid outside Custom..EndCustm or ToolBar..EndTbar blocks For example, an Item command is attempted outside a Custom or ToolBar structure. 530 Invalid outside Dialog..EndDlog, Custom..EndCustm, or ToolBar..EndTBar blocks For example, a Title command is attempted outside a Dialog, Custom, or ToolBar structure. 540 Invalid outside Dialog..EndDlog block For example, the DropDown command is attempted outside a Dialog structure. 550 Invalid outside function or program A number of commands are not valid outside a program or a function. For example, Local cannot be used unless it is in a program or function.

Appendix B: Reference Information 545

Error Number Description

560 Invalid outside Loop..EndLoop, For..EndFor, or While..EndWhile blocks For example, the Exit command is valid only inside these loop blocks.

570 Invalid pathname For example, \var is invalid.

575 Invalid polar complex

580 Invalid program reference Programs cannot be referenced within functions or expressions such as 1+p(x) where p is a program.

590 Invalid syntax block A Dialog..EndDlog block is empty or has more than one title. A Custom..EndCustm block cannot contain PIC variables, and items must be preceded by a title. A Toolbar..EndTBar block must have a second argument if no items follow; or items must have a second argument and must be preceded by a title.

600 Invalid table

605 Invalid use of units

610 Invalid variable name in a Local statement

620 Invalid variable or function name

630 Invalid variable reference

640 Invalid vector syntax

650 Link transmission A transmission between two units was not completed. Verify that the connecting cable is connected firmly to both units.

665 Matrix not diagonalizable

670 Memory 673 The calculation required more memory than was available at that time. If you get this error when you run a large program, you may need to break the program into separate, smaller programs or functions (where one program or function calls another).

680 Missing (

546 Appendix B: Reference Information

Appendix B: Reference Information 547

Error Number Description

850 Program not found A program reference inside another program could not be found in the provided path during execution.

860 Recursion is limited to 255 calls deep

870 Reserved name or system variable

875 ROM-resident routine not available

880 Sequence setup

885 Signature error

890 Singular matrix

895 Slope fields need one selected function and are used for 1st-order equations only

900 Stat

910 Syntax The structure of the entry is incorrect. For example, x+-y (x plus minus y) is invalid; whereas, x+ -y (x plus negative y) is correct.

930 Too few arguments The expression or equation is missing one or more arguments. For example, d(f(x)) is invalid; whereas, d(f(x),x) is the correct syntax.

940 Too many arguments The expression or equation contains an excessive number of arguments and cannot be evaluated.

950 Too many subscripts

955 Too many undefined variables

960 Undefined variable

965 Unlicensed product software or Flash application

970 Variable in use so references or changes are not allowed

980 Variable is locked, protected, or archived

990 Variable name is limited to 8 characters

1000 Window variables domain

1010 Zoom

548 Appendix B: Reference Information

Error Number Description

Warning: ∞^0 or undef^0 replaced by 1 Warning: 0^0 replaced by 1 Warning: 1^∞ or 1^undef replaced by 1 Warning: cSolve may specify more zeros Warning: May produce false equation Warning: Expected finite real integrand Warning: May not be fully simplified Warning: More solutions may exist Warning: May introduce false solutions Warning: Operation may lose solutions Warning: Requires & returns 32 bit value Warning: Overflow replaced by ∞ or -∞ Warning: Questionable accuracy Warning: Questionable solution Warning: Solve may specify more zeros Warning: Trig argument too big to reduce

Appendix B: Reference Information 549

Modes

This section describes the modes of the TI-89 / TI-92 Plus and lists the possible settings of each mode. These mode settings are displayed when you press [MODE].

Graph

Specifies the type of graphs you can plot.

Note: If you use a split screen with Number of Graphs = 2, Graph is for the top or left part of the screen and Graph 2 is for the bottom or right part.

Current Folder

Specifies the current folder. You can set up multiple folders with unique configurations of variables, graph databases, programs, etc.

Note: For detailed information about using folders, see Chapter 5.

Display Digits

Selects the number of digits. These decimal settings affect only how results are displayed—you can enter a number in any format.

Internally, the TI-89 / TI-92 Plus retains decimal numbers with 14 significant digits. For display purposes, such numbers are rounded to a maximum of 12 significant digits.

550 Appendix B: Reference Information

Angle

Specifies the units in which angle values are interpreted and displayed in trig functions and polar/rectangular conversions.

1:RADIAN
2:DEGREE

Exponential Format

Specifies which notation format should be used. These formats affect only how an answer is displayed; you can enter a number in any format. Numeric answers can be displayed with up to 12 digits and a 3-digit exponent.

1:NORMAL
Expresses numbers in standard format. For example, 12345.67

2:SCIENTIFIC
Expresses numbers in two parts:

• The significant digits display with one digit to the left of the decimal.
• The power of 10 displays to the right of E.
  For example, 1.234567E4 means 1.234567×10⁴

3:ENGINEERING
Similar to scientific notation. However:

• The number may have one, two, or three digits before the decimal.
• The power-of-10 exponent is a multiple of three.
  For example, 12.34567E3 means 12.34567×10³

Note: If you select NORMAL, but the answer cannot be displayed in the number of digits selected by Display Digits, the TI-89 / TI-92 Plus displays the answer in SCIENTIFIC notation. If Display Digits = FLOAT, scientific notation will be used for exponents of 12 or more and exponents of –4 or less.

Complex Format

Specifies whether complex results are displayed and, if so, their format.

1:REAL
Does not display complex results. (If a result is a complex number and the input does not contain the complex unit i, an error message is displayed.)

2:RECTANGULAR
Displays complex numbers in the form: a+bi

3:POLAR
Displays complex numbers in the form: re^iθ

Appendix B: Reference Information 551

Vector Format

Determines how 2-element and 3-element vectors are displayed. You can enter vectors in any of the coordinate systems.

Pretty Print

Determines how results are displayed on the Home screen.

Note: For a complete description of these settings, refer to “Formats of Displayed Results” in Chapter 2.

Split Screen

Lets you split the screen into two parts. For example, you can display a graph and see the Y= Editor at the same time (Chapter 14).

To determine what and how information is displayed on a split screen, use this mode in conjunction with other modes such as Split 1 App, Split 2 App, Number of Graphs, and Split Screen Ratio. (Split Screen Ratio is available on the TI-92 Plus only.)

552 Appendix B: Reference Information

Split 1 App and Split 2 App

Specifies which application is displayed on the screen.

• For a full screen, only Split 1 App is active.
• For a split screen, Split 1 App is the top or left part of the screen and Split 2 App is the bottom or right part.

The available application choices are those listed when you press ◀ from the Page 2 mode screen or when you press [APPS]. You must have different applications in each screen unless you are in 2-graph mode.

Number of Graphs

Specifies whether both parts of a split screen can display graphs at the same time.

Graph 2

Specifies the type of graphs that you can plot for the second graph on a two-graph split screen. This is active only when Number of Graphs = 2. In this two-graph setting, Graph sets the type of graph for the top or left part of the split screen, and Graph 2 sets the bottom or right part. The available choices are the same as for Graph.

Split Screen Ratio (TI-92 Plus only)

Specifies the proportional sizes of the two parts of a split screen.

Exact/Approx

Specifies how fractional and symbolic expressions are calculated and displayed. By retaining rational and symbolic forms in the EXACT setting, the TI-89 / TI-92 Plus increases precision by eliminating most numeric rounding errors.

Note: For a complete description of these settings, refer to “Formats of Displayed Results” in Chapter 2.

Appendix B: Reference Information 553