Overview
This lecture demonstrates how to use the VARS button on the TI-84 calculator to efficiently evaluate function values and numerically investigate limits.
Using the VARS Button for Function Evaluation
- Enter the given function into the calculator using the Y= button (e.g., enter 1/(x-7) as Y1).
- Use parentheses around the denominator to avoid calculation errors.
- After entering the function, press 2nd MODE to return to the home screen for calculations.
- Access the y-VARS menu by pressing VARS, arrowing to Y-VARS, and selecting Function, then Y1.
- To evaluate the function at a specific x-value, type Y1(value) (e.g., Y1(7.1)).
- Use 2nd ENTER to recall and edit previous entries for quick substitution of new x-values.
Numerical Limit Investigation Example
- To estimate the limit as x approaches 7 for f(x) = 1/(x-7), substitute values just greater than 7 (e.g., 7.1, 7.01, 7.001, 7.0001) to observe outputs increasing (10, 100, 1000, 10000).
- Function values increase without bound as x approaches 7 from the right, indicating the right-hand limit does not exist and tends toward positive infinity.
- Substitute values just less than 7 (e.g., 6.9, 6.99, 6.999, 6.9999) to observe outputs decreasing (-10, -100, -1000, -10000).
- Function values decrease without bound as x approaches 7 from the left, indicating the left-hand limit does not exist and tends toward negative infinity.
- Since the right- and left-hand limits approach different infinities, the two-sided limit at x = 7 does not exist.
Key Terms & Definitions
- VARS button — a key on the TI-84 calculator used to access stored functions and variables.
- Y-VARS menu — the calculator menu that lists functions stored in the Y= editor (e.g., Y1, Y2).
- Limit — the value that a function approaches as the input approaches a certain point.
- One-sided limit — the value a function approaches from one side (left or right) of a point.
- Infinite behavior — when function values increase or decrease without bound as x approaches a specific value.
Action Items / Next Steps
- Practice entering and evaluating functions using the VARS and Y-VARS features on your calculator.
- Try estimating limits numerically for other functions using values close to the point of interest.