determine whether each of these functions is o(x^2 ).
(a) 100x + 1000
(b) 100x^(2) + 1000
(c) (x^(3)/100) ? 1000x^(2)
(d) x log x

Step-by-step explanation:

"Of the order x^2" means the dominant behavior matches that of x^2 as x gets large. For polynomial functions, the dominant behavior is that of the highest-degree term.

For other functions, the dominant behavior will typically be governed in some other way. Here, the rate of growth of the x·log(x) function is determined by log(x), which has decreasing slope as x increases.

Only answer selection B has a highest-degree term of x^2, so only that one exhibits O(x^2) behavior.

2 equivalent expressions to represent the area of a rectangle and the top is n-3 and the side is 2

area of the rectangle = length * width

given length = n - 3

width = 2

replace it in the area

so area of the rectangle = (n-3) *2

= 2(n-3)

one of the expression is 2(n-3)

to get another expression we distribute 2 inside the parenthesis

2(n-3) is 2n - 6

so another expression is 2n - 6

two equivalent expression are

2(n - 3)   , 2n - 6