Determine the big-O notation for the following:a. 5n5/2 + n2/5b. 6log(n) + 9nc. 3n4 + nlog(n)d. 5n2 + n3/2
Question
Determine the big-O notation for the following:a. 5n5/2 + n2/5b. 6log(n) + 9nc. 3n4 + nlog(n)d. 5n2 + n3/2
Solution
To determine the big-O notation for each of the given expressions, we need to analyze the growth rate of the functions as the input size (n) increases.
a. 5n^(5/2) + n^(2/5): The dominant term in this expression is 5n^(5/2) since it has a higher exponent. Therefore, the big-O notation for this expression is O(n^(5/2)).
b. 6log(n) + 9n: Both terms in this expression have different growth rates. The logarithmic term, 6log(n), grows at a slower rate compared to the linear term, 9n. Therefore, the dominant term is 9n. Hence, the big-O notation for this expression is O(n).
c. 3n^4 + nlog(n): In this expression, the dominant term is 3n^4 since it has the highest exponent. The logarithmic term, nlog(n), grows at a slower rate compared to the polynomial term. Therefore, the big-O notation for this expression is O(n^4).
d. 5n^2 + n^(3/2): The dominant term in this expression is n^(3/2) since it has a higher exponent. Therefore, the big-O notation for this expression is O(n^(3/2)).
In summary: a. O(n^(5/2)) b. O(n) c. O(n^4) d. O(n^(3/2))
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