SUMMARY
The limit of the rational function lim_x->∞ of [√x + 2|x|] / [1 + x] evaluates to ±2. The user correctly divided the numerator and denominator by the highest power of x, simplifying the expression to [x^-1/2 +/- 2] / [1/x + 1]. As x approaches infinity, the limit simplifies to [0 +/- 2] / [0 + 1], confirming that the limit is indeed ±2, with the clarification that x is positive as it approaches +∞.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with rational functions
- Knowledge of asymptotic behavior of functions
- Basic algebraic manipulation of expressions
NEXT STEPS
- Study the properties of limits involving infinity
- Learn about L'Hôpital's Rule for indeterminate forms
- Explore the concept of asymptotic analysis in calculus
- Review the behavior of square root functions as x approaches infinity
USEFUL FOR
Students studying calculus, particularly those focusing on limits and rational functions, as well as educators looking for examples of limit evaluations involving infinity.