Find the least integer n such that f(x) is O(x^n) for each of these functions.

$f(x)=2x^{2}+x^{3}log x$ $f(x)=3x^{5}+(log x)^{4}$ $f(x)=dfrac{x^{4}+x^{2}+1}{x^{4}+1}$ The article aims to find the value of the n for each function given to satisfy the O(x^n) notation. Big-O notation represents the maximum operating time of the algorithm. Therefore, it provides the worst possible algorithm. In computer science, big O notation is used to classify algorithms according to how their working time or […]

12/5 as a mixed number.

How to represent the given improper fraction as a mixed number. The main objective of this question is to represent the given improper fraction as a mixed number. This question uses the concept of improper fractions and mixed numbers. In an improper fraction, the value of the numerator is always greater than the value of […]

3.16 repeating as a fraction. Convert 3.16 to a fraction.

This question aims to find the repeating number $ 3.16 $ as a fraction. Fraction is any number written in the form of a quotient. In the quotient, any integer written above is called the numerator and the integer written below is called the denominator. An integer can be any real number or complex number. If […]

Write an algebraic expression for: 6 more than a number c.

  This problem aims to find an algebraic expression for a given verbal expression, using the knowledge of simple mathematics and some commonly known algebraic and arithmetic techniques. This kind of problem requires the understanding of the keywords that are used in mathematics as a way to express algebraic terminology. Similarly, some problems are so […]

The amount 180.00 is what percent greater than 135.00?

The question aims to find the percent increase in an amount. Percent increase depends on relative change. The relative difference and relative change are used to compare two quantities in consideration of the “size” of what is being compared. Comparisons are expressed as ratios and are unitless numbers. The terms rate of change, percentage (age) […]