TI-89 Limit: Overview
The limit for this function is 0 at x = 0, and ∞ for x = ∞
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) = (x2 – 4) / (x2 + 6)
Step 1: Press the HOME key.
Step 2: Press the F3 button and then press 3 to select the “limit” command.
Step 3: Press Type your function into the calculator, followed by: comma x comma 8. Don’t forget to close your parentheses.
Step 4: Press ENTER .
The solution is 6/7, or .857.
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) = (x3 + 7) / (x2 + 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:
Clausen, C. Applications of Calculus I: Chemical Kinetics The Derivative as a Function
.
Larson & Edwards. Calculus.
Stephanie Glen. "TI-89 Limit in Easy Steps" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/ti-89-limits-in-easy-steps/
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