Final answer:
The limit of 1/(-3) as it approaches negative infinity is equal to zero.
Step-by-step explanation:
The given expression represents the limit of 1 divided by the constant value -3 as the variable approaches negative infinity. Evaluating this limit involves understanding the behavior of the function as the input tends toward negative infinity. As the denominator remains a constant value (-3), and the numerator (1) doesn't change, dividing a constant by an increasingly large negative number leads to the result approaching zero. Mathematically, this behavior is represented as the limit of 1/(-3) as x approaches negative infinity equals zero, denoted as lim(x→-∞) 1/(-3) = 0.
In calculus, determining limits involves examining the function's behavior as the independent variable approaches a particular value or infinity. In this case, when the variable tends toward negative infinity, the fraction 1/(-3) gets closer and closer to zero. This occurs because no matter how large the negative number becomes, dividing a constant (1) by it results in a smaller and smaller positive value, approaching zero but never actually reaching it. Therefore, the limit of 1/(-3) as x approaches negative infinity is zero.
Understanding the concept of limits and how functions behave as the input approaches certain values or infinity is crucial in calculus and mathematical analysis. In this case, recognizing that a constant divided by an increasingly large negative value tends towards zero allows us to confidently determine the limit as zero. This understanding aids in evaluating functions and their behavior in various mathematical contexts and real-world applications.