# Answer: Limit of Big-O Terms: O(1/x) & O(x)

• Avichal
In summary, a limit of big-O terms represents the behavior of a function as the input approaches infinity and indicates the upper bound or worst-case scenario for its growth rate. O(1/x) is a constant function, while O(x) is a linear function. To calculate the limit of big-O terms, you need to determine the highest power of the input variable in the function. O(1/x) and O(x) have an inverse relationship, with O(1/x) growing slower than O(x) as the input size increases.
Avichal
I'm a bit confused with limits of big-O terms. What should be the answer for following:-
1) limit of O(1/x) as x->0. O(1) maybe but I'm not sure.
2) limit of O(x) as x-> 0. O(1) or 0?

The capital O symbol means that you quantity "behaves" like some other quantity in a certain limit. So, $O(1/x)$ behaves as $1/x$ and therefore goes to infinity as x approaches 0. For the same reason $O(x)\to 0$ as x approaches 0.

## 1. What is a limit of big-O terms?

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.

## 2. What is O(1/x)?

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.

## 3. What is O(x)?

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.

## 4. How do you calculate the limit of big-O terms?

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.

## 5. What is the relationship between O(1/x) and O(x)?

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).

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