SUMMARY
The limit problem presented involves evaluating the expression lim (√8(a+h) - √8a)/h as h approaches 0. The solution requires applying the technique of multiplying the numerator and denominator by the conjugate, specifically [√8(a+h) + √8a]. This method simplifies the expression and eliminates the variable h, allowing for the limit to be determined accurately. The final result reveals the derivative of the function at the point a, confirming the application of calculus principles.
PREREQUISITES
- Understanding of calculus concepts, specifically limits and derivatives.
- Familiarity with algebraic manipulation, including rationalizing expressions.
- Knowledge of the properties of square roots and their behavior in limits.
- Experience with evaluating limits involving indeterminate forms.
NEXT STEPS
- Study the process of rationalizing expressions in calculus.
- Learn about the formal definition of a derivative and its applications.
- Explore advanced limit techniques, such as L'Hôpital's Rule.
- Practice solving similar limit problems involving square roots and algebraic expressions.
USEFUL FOR
Students studying calculus, particularly those focusing on limits and derivatives, as well as educators looking for examples of limit evaluation techniques.