A limit of big-O terms refers to the behavior of a function as its input approaches infinity. In big-O notation, it represents the upper bound or worst-case scenario for the growth rate of a function.
O(1/x) is a big-O term that represents a constant function. It indicates that the growth rate of the function is bounded by a constant value as the input increases.
O(x) is a big-O term that represents a linear function. It indicates that the growth rate of the function is directly proportional to the input size.
To calculate the limit of big-O terms, you need to determine the highest power of the input variable in the function. The limit will be the coefficient of that power. For example, in O(1/x), the limit would be 1 since x is raised to the power of -1.
O(1/x) and O(x) have an inverse relationship. As the input size increases, O(1/x) approaches 0, while O(x) approaches infinity. This means that O(1/x) grows slower than O(x).