SUMMARY
The limit of csc(2x) as x approaches π/2 from the right side is negative infinity. This conclusion is drawn from analyzing the behavior of the cosecant function near its vertical asymptotes. While the graph suggests a positive infinity, the correct interpretation aligns with the textbook's assertion due to the function's properties as it approaches the asymptote from the right. The discrepancy highlights the importance of understanding the direction of approach in limit calculations.
PREREQUISITES
- Understanding of trigonometric functions, specifically cosecant.
- Familiarity with limits and asymptotic behavior in calculus.
- Ability to interpret graphical representations of functions.
- Knowledge of the unit circle and angle measures in radians.
NEXT STEPS
- Study the properties of trigonometric functions, focusing on cosecant and its asymptotes.
- Learn about limits approaching vertical asymptotes in calculus.
- Explore graphing techniques for trigonometric functions using tools like Desmos or GeoGebra.
- Review examples of limit problems involving trigonometric functions in calculus textbooks.
USEFUL FOR
Students studying calculus, particularly those focusing on limits and trigonometric functions, as well as educators seeking to clarify common misconceptions in limit evaluations.