TI-89 Calculus: Sequences, Series and More

TI-89 calculus is the main reason the handheld is still on supply lists: the CAS differentiates, integrates and takes limits exactly, not just numerically. This article maps what the TI-89 Titanium can do in calculus, from the first derivative to sequences and series, and where the separate Calculus Tools App fits in.

The core: d(, ∫( and limit(

Three commands cover most of Calculus I and II. d( is 2nd 8, ∫( is 2nd 7, and limit( is item 3 in the F3 Calc menu. All three take the expression first and the variable second. ∫( takes two more arguments for the bounds of a definite integral, and limit( takes the point.

2nd8→ d(

2nd7→ ∫(

F33→ limit(

Derivative, integral and limit examples
Input	Result
d(x^3,x)	3·x²
∫(x,x)	x²/2
limit(sin(x)/x,x,0)	1
nInt(x^2,x,0,1)	0.333333333333

The answers are exact. For a decimal, press ◆ ENTER, or use the numeric commands such as nInt( in the last row. The AP Calculus guide goes through each of these with more examples.

Applications: extrema, tangent lines, arc length

The F3 Calc menu also holds the tools for typical application questions. fMin( and fMax( return the x value of a minimum or maximum, and arcLen( takes the same four arguments as a definite integral. Calc89 also accepts tangentLine( on the home line, which the handheld offers on the graph screen under F5 Math, Tangent.

F36→ fMin(

Extrema, tangent line and arc length examples
Input	Result
fMin(x^2-4x,x)	x=2
fMax(-x^2+2x,x)	x=1
tangentLine(x^2,x,1)	2·x−1
arcLen(x^(3/2),x,0,4)	80·√10/27−8/27

For differential equations, deSolve( sits in the same F3 Calc menu. It has its own guide.

F3then scroll to deSolve( and pressENTER

Sequences

A sequence on the TI-89 Titanium is a list built by a rule. seq( takes the expression, the index variable, the first and the last index, and an optional step. It lives in the MATH menu under List.

2nd53►►►9→ seq(

Sequence example
Input	Result
seq(n^2,n,1,5)	{1,4,9,16,25}

To see whether a sequence converges, take the limit of its rule with limit( and ∞ as the point. ∞ is ◆ CATALOG. To draw the terms, set Graph to SEQUENCE in MODE: the Y= editor then asks for sequence rules instead of functions, and the graph shows the terms as points.

◆CATALOG→ ∞

Series and Taylor polynomials

For sums, Σ( is item 4 in F3 Calc: Σ(expression, index, start, end). The end may be ∞ for an infinite series, and the CAS returns the exact sum when it can find one. For power series, taylor( gives the Taylor polynomial of a given order around a point, 0 by default. Calc89 also has series(, which returns the series expansion up to the given order.

F34→ Σ(

F3then scroll to taylor( and pressENTER

Sum, Taylor polynomial and series examples
Input	Result
Σ(k,k,1,10)	55
taylor(ℯ^(x),x,4)	x⁴/24+x³/6+x²/2+x+1
series(sin(x),x,5)	x⁵/120−x³/6+x

The Taylor polynomial of e^x up to order 4 and the expansion of sin(x) up to order 5 are the two series every BC student meets. Comparing a function with its Taylor polynomial on the graph screen is a quick way to see where the approximation is good.

The Calculus Tools App: what it adds

Texas Instruments offers a separate Calculus Tools App for the TI-89 Titanium. Its page says that it “allows students to explore calculus concepts more in depth, than can be explored with their TI calculator alone” and lists “Sequences, Series, Vector calculus, Fourier series, And more!” It is an exploration tool: it walks through concepts interactively, while the commands above compute results.

Here is how those topics map to Calc89:

Sequences: yes, with seq(, limit( and the sequence graph mode.
Series: yes, with Σ(, taylor( and series(.
Vector calculus: no dedicated tool. Calc89 has the vector commands dotP(, crossP(, unitV( and norm(, and you can differentiate each component with d(, but there is no app for gradient fields, line integrals or flux.
Fourier series: no. Calc89 has no Fourier tool. You can still type the coefficient integrals of a Fourier series with ∫( and evaluate them one by one.

Vector examples
Input	Result
dotP([1,2,3],[4,5,6])	32
crossP([1,0,0],[0,1,0])	001

If your course depends on Fourier series or vector fields, the CAS on either device is a helper for single steps, not a complete tool.

In Calc89

Every command in this article uses the same name, argument order and keys in Calc89, so the examples work as typed. Results appear in textbook form, with fractions, roots and exponents set the way your book prints them. The camera problem scanner reads a printed or handwritten integral or limit and puts it on the home line in CAS syntax, and the AI keystroke tutor shows the key sequence for a problem step by step. Calc89 is free to download, with Pro features as an in-app purchase.

As of October 2026, phone and tablet apps are not permitted on standardized exams. The AP Calculus and AP Physics exams permit the physical TI-89 Titanium, while the SAT (since August 2025) and the ACT prohibit CAS calculators, including the TI-89 Titanium. Practice with Calc89, take the handheld to the AP exam.

Frequently asked questions

Do I need the Calculus Tools App to do calculus on the TI-89?

No. Derivatives, integrals, limits, sums, sequences and Taylor polynomials are built into the CAS. The app adds interactive explorations on top.

Can Calc89 compute Fourier series?

No. Calc89 has no Fourier series tool. It covers sequences, sums, Taylor polynomials and series expansions with seq(, Σ(, taylor( and series(.

Is the TI-89 Titanium allowed on the AP Calculus exam?

Yes. As of October 2026, the AP Calculus AB and BC exams permit the physical TI-89 Titanium. Phone apps are not permitted.

What the TI-89 Titanium Can Do in Calculus: Sequences, Series and More