SUMMARY
The limit of the function 3x/(5-x) as x approaches 5 from the right (5+) is confirmed to be negative infinity. As x approaches 5, the denominator (5-x) approaches zero from the negative side, resulting in a division by a very small negative number. Consequently, the expression evaluates to 15 divided by a value approaching zero, leading to the conclusion that the limit is indeed negative infinity.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with rational functions
- Knowledge of approaching limits from the left and right
- Basic algebraic manipulation skills
NEXT STEPS
- Study the concept of one-sided limits in calculus
- Explore the behavior of rational functions near vertical asymptotes
- Learn about the epsilon-delta definition of limits
- Investigate other examples of limits approaching infinity
USEFUL FOR
Students studying calculus, particularly those focusing on limits and rational functions, as well as educators looking for examples to illustrate limit behavior in mathematical analysis.