SUMMARY
The limit statement lim x→2 f(4x^2 − 11) = 8 is evaluated based on the continuity of the function f at the point 5, where f(5) = 8 and f(4) = 3. Since g(x) = 4x^2 - 11 is continuous and approaches 5 as x approaches 2, the composition of the continuous functions confirms that lim x→2 f(4x^2 − 11) indeed equals f(5), which is 8. Therefore, the statement is true.
PREREQUISITES
- Understanding of limits and continuity in calculus
- Familiarity with function composition
- Knowledge of the properties of continuous functions
- Basic algebraic manipulation of polynomial functions
NEXT STEPS
- Study the properties of continuous functions in calculus
- Learn about function composition and its implications for limits
- Explore the concept of limits approaching specific values
- Review examples of polynomial functions and their limits
USEFUL FOR
Students studying calculus, particularly those focusing on limits and continuity, as well as educators looking for examples of limit evaluation techniques.