Assume the domain of the function is {1,2,3,...}. Determine the theta notation for the function f(n)=7n^2+4n+2
1 answer:
We have that O(n²) is the theta notation for 7n² + 4n + 2.
Let's give big-Oh a formal definition:
O(g(n)) = {the set of all f such that 0 f(n)
cg(n) for any n >= n₀ fulfilling positive constants c and n₀}
To show this
We need to find c and n₀ such that:
7n² + 4n + 2 <= cn² for all n >= n₀ .
Divide both sides by n², getting:
7 + 4/n + 2/(n²) <= c for all n >= n₀ .
If we choose n₀ equal to 1, then we need a value of c such that:
7 + 4 + 2 <= c
We can set c equal to 13. Now we have:
7n² + 4n + 2 <= 13n² for all n >= 1 .
Hence, 7n² + 4n + 2=O(n²)
Learn more about Big-Oh notation here-
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Answer:
1. 0.20 m, 200 mm
2. 152 cm, 1520 mm
Step-by-step explanation:
You may be familiar with a place-value chart that names the digits of a number based on their relationship to the decimal point. It might look like ...
(units) . (tenths) (hundredths) (thousandths)
So a number like 0.2 units can be rewritten in terms of hundredths or thousandths like this:
0.200 units = 20.0 hundredths = 200. thousandths
The name that's attached depends on where you put the decimal point.
___
When the units are meters, the corresponding names are ...
(meters) . (decimeters) (centimeters) (millimeters)
1. That is 0.200 meters = 20.0 centimeters = 200. millimeters.
2. 1.520 meters = 152.0 centimeters = 1520. millimeters.
