Finding Big-O of sqrt(x^3+x^2+3) - Is Reverse the Same?

Thread starter shahin93
Start date Feb 25, 2012

In summary, the Big-O notation is a mathematical notation used to analyze the time complexity or space complexity of an algorithm as the input size approaches infinity. To find the Big-O of a function, the dominant term is identified while ignoring constant coefficients and lower-order terms. The function in question is sqrt(x^3+x^2+3) with an input size of x. The reverse of this function, sqrt(3)+x+3x^2, has a different Big-O notation and limiting behavior as the input size approaches infinity.

Feb 25, 2012

shahin93

Homework Statement

how do i find the least n such that

sqrt(x^3+x^2+3) is O(x^n)?

is the reverse the same?

Physics news on Phys.org

Feb 25, 2012

tiny-tim

Science Advisor

Homework Helper

hi shahin93!

try it for x = 10, then x = 100, then x = 100000 …

you'll soon get the hang of what n needs to be

1. What is the Big-O notation?

The Big-O notation is a mathematical notation that represents the limiting behavior of a function when the input size approaches infinity. It is used to analyze the time complexity or space complexity of an algorithm.

2. How do you find the Big-O of a function?

To find the Big-O of a function, we look at the dominant term in the function as the input size approaches infinity. We ignore any constant coefficients and lower-order terms. The resulting notation is the Big-O of the function.

3. What is the function in question?

The function in question is sqrt(x^3+x^2+3).

4. What is the input size for this function?

The input size for this function is x, where x is a positive integer.

5. Is the reverse of this function the same?

No, the reverse of this function is not the same. The reverse of sqrt(x^3+x^2+3) is 3x^2+x+sqrt(3), which has a different Big-O notation and therefore a different limiting behavior as the input size approaches infinity.