Show that 8x3 + 12x + 100 logx is O(x3).

Step 1</p>

For two given functions and , we can say that is if and only if there exists two constants B and l , such that whenever .

In this problem we are asked to show that is .

Step 2</p>

For two given functions and , if is and is , then the sum of the two functions is .

First we will estimate .

We can write that for

Multiplying both sides by x, we get

Since we can write

Adding both sides, we get

which is same as .

Since for , we can write that

for

Therefore with witnesses and , is .

To estimate , we do as follows

We know that , hence we write

for

Since for , we can write that

for

Therefore with witnesses and ,is .