## TI-89 Limit: Overview

A “limit” is the value a function “approaches” as the input or index (usually the x-value) approaches some specified value. In other words, it’s a theoretical point where your function maxes out. Some functions don’t actually reach a certain value; they come close, but not quite.

## Syntax

With its **limit command**, the TI-89 makes it a snap to evaluate limits. The syntax for the function is:

**limit (expression, variable, value)**.

- “Expression” is just the equation your want to find the limit for.
- “Variable” is nearly always going to be x (although check your equation!)
- “value” is where you want to find the limit.

**You can access the limit() function in three different ways (which all access the same command):**

- Press F3 (Calc) and then 3 (see worked example below).
- Look in the Catalog (press l to go to the start of the l section).
- Press 2nd, then MATH. Look in the “A:Calculus” submenu.

## TI-89 Limit Example 1

**Example problem:** **Evaluate the limit** as x approaches 8 for the following function.

f(x) = (x^{2} – 4) / (x^{2} – 6)

Step 1: Press the HOME key.

Step 2: Press the F3 button and then press 3 to select the “limit” command.

Step 3: Type your function into the calculator, followed by:

**, x , 8 ) **

We’re typing “x” here and then “8” because that’s where we’re evaluating the limit (at x = 8).

Make sure to use parentheses correctly to ensure the right order of operations.

*Don’t forget to close your parentheses.*

Step 4: Press ENTER .

The solution is 15/14.

The nice thing about the TI-89 is that after you’ve typed in your function and pressed ENTER, it will give you the limit *and* show you what function you’ve evaluated, so you know you’ve typed in the right formula!

Sometimes your problem might be phrased differently, as in this next example.

## Limit Example 2

**Example problem:** **Describe the limits** of the function f(x) = (x^{3} + 7) / (x^{2} + 3) symbolically as x approaches 0.

Step 1: Press the HOME key.

Step 2: Press F3 and then 3 to select the limit command.

Step 3: Press ( X ^ 3 + 7 ) ÷ ( X ^ 2 + 3 ) , X , 0

Step 4: Press ENTER.

The solution is 7/3 or 2.3333.

**Tips:**

- If you get the error “too few arguments,” make sure you have entered the correct amount of parentheses.
- The “X” variable and the multiplication symbol “x” look almost identical on the TI-89 keypad. Make sure you are pressing the right key—look to the equation to ensure you have typed the correct function into the calculator.

That’s how to find a TI-89 Limit. You’re done!

**References:**

TI-89 Simulator (Images).

Clausen, C. Applications of Calculus I: Chemical Kinetics The Derivative as a Function

.

Larson & Edwards. Calculus.