The limit of the function f(x) = x^(5/3) - 5x^(2/3) as x approaches both positive and negative infinity is determined by the dominating term, which is x^(5/3). By factoring out x^(5/3), the expression simplifies to f(x) = x^(5/3)(1 - x^(-1)). As x approaches positive infinity, the limit approaches positive infinity, while as x approaches negative infinity, the limit approaches negative infinity. This analysis confirms that the behavior of the function is primarily influenced by the highest degree term.
PREREQUISITESStudents of calculus, mathematicians, and anyone interested in understanding the behavior of polynomial functions at infinity.