SUMMARY
The limit \(\lim_{x\rightarrow \infty} {\frac{3x+5}{x-4}}\) can be solved by dividing both the numerator and denominator by \(x\). This simplifies the expression to \(\lim_{x\to\infty} \frac{3+ \frac{5}{x}}{1- \frac{4}{x}}\). As \(x\) approaches infinity, the terms \(\frac{5}{x}\) and \(\frac{4}{x}\) approach 0, resulting in a final limit value of 3.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with algebraic manipulation of fractions
- Knowledge of asymptotic behavior of functions
- Basic proficiency in mathematical notation
NEXT STEPS
- Study the concept of limits in calculus
- Learn about L'Hôpital's Rule for indeterminate forms
- Explore asymptotic analysis in mathematical functions
- Practice solving various limit problems using algebraic techniques
USEFUL FOR
Students studying calculus, mathematics educators, and anyone looking to improve their understanding of limits and asymptotic behavior in functions.