Overview
This lecture demonstrates how to use limit properties to evaluate the limit as x approaches 6 for the function cube root of (2 + x).
Applying Limit Properties
- The given limit is limₓ→6 ³√(2 + x).
- The limit of a root equals the root of the limit, especially for odd roots like the cube root.
- Rewrite as ³√(limₓ→6 (2 + x)).
Breaking Down the Limit
- Apply the sum property: limₓ→6 (2 + x) = limₓ→6 2 + limₓ→6 x.
- The limit of a constant (limₓ→6 2) is just 2.
- The limit of x as x approaches 6 (limₓ→6 x) is 6.
Calculating the Final Answer
- Substitute the values: ³√(2 + 6) = ³√8.
- Evaluate ³√8, which equals 2.
Key Terms & Definitions
- Limit Property (root) — The limit of a root is the root of the limit (works for odd roots).
- Sum Property of Limits — The limit of a sum equals the sum of the limits.
Action Items / Next Steps
- Practice applying limit properties to other functions.
- Review properties of limits in your textbook.