SUMMARY
The limit of the expression x/(sqrt(1+3x)-1) as x approaches 0 can be evaluated using algebraic manipulation. The key step involves multiplying the expression by (sqrt(1+3x)+1)/(sqrt(1+3x)+1) to eliminate the indeterminate form. After simplification, the limit resolves to 1/3, as the x terms cancel out and the remaining expression approaches 1/3 as x approaches 0.
PREREQUISITES
- Understanding of limit laws in calculus
- Familiarity with algebraic manipulation techniques
- Knowledge of square root functions and their properties
- Basic skills in simplifying rational expressions
NEXT STEPS
- Study the application of L'Hôpital's Rule for indeterminate forms
- Learn about Taylor series expansions for approximating limits
- Explore the concept of continuity and its relation to limits
- Practice solving limits involving square roots and rational functions
USEFUL FOR
Students studying calculus, mathematics educators, and anyone seeking to improve their skills in evaluating limits and simplifying expressions in calculus.
