Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the following three functions.f1 = 1...
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Consider the following three functions.
f1 = 10n
f2 = nlogn
f3 = n√n
Which one of the following options arranges the functions in the increasing order of asymptotic growth rate?
- a)f3,f2,f1
- b)f2,f1,f3
- c)f1,f2,f3
- d)f2,f3,f1
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Consider the following three functions.f1 = 10nf2 = nlognf3 = n√...
Understanding Asymptotic Growth Rates
To compare the growth rates of the functions f1, f2, and f3, we need to analyze them as n approaches infinity.
Functions Overview
- f1 = 10n: This function grows linearly with n.
- f2 = n log n: This function grows faster than linear but slower than polynomial functions. The logarithmic factor increases the growth rate compared to f1.
- f3 = n√n: This can be rewritten as n^(3/2), a polynomial function that grows faster than both f1 and f2.
Comparing Growth Rates
- f1 vs f2: As n becomes very large, log n grows; thus, n log n grows faster than 10n. Therefore, f2 is greater than f1 for large n.
- f2 vs f3: f3 = n√n = n^(3/2) grows faster than n log n. For sufficiently large n, the polynomial term dominates the logarithmic term, making f3 greater than f2.
- f1 vs f3: Since f3 is n^(3/2) and f1 is linear, f3 will always grow faster than f1 as n increases.
Conclusion
Arranging the functions in increasing order of growth rates, we have:
- f2 (n log n)
- f3 (n√n)
- f1 (10n)
Thus, the correct order is f2, f3, f1, which corresponds to option 'D'.
To compare the growth rates of the functions f1, f2, and f3, we need to analyze them as n approaches infinity.
Functions Overview
- f1 = 10n: This function grows linearly with n.
- f2 = n log n: This function grows faster than linear but slower than polynomial functions. The logarithmic factor increases the growth rate compared to f1.
- f3 = n√n: This can be rewritten as n^(3/2), a polynomial function that grows faster than both f1 and f2.
Comparing Growth Rates
- f1 vs f2: As n becomes very large, log n grows; thus, n log n grows faster than 10n. Therefore, f2 is greater than f1 for large n.
- f2 vs f3: f3 = n√n = n^(3/2) grows faster than n log n. For sufficiently large n, the polynomial term dominates the logarithmic term, making f3 greater than f2.
- f1 vs f3: Since f3 is n^(3/2) and f1 is linear, f3 will always grow faster than f1 as n increases.
Conclusion
Arranging the functions in increasing order of growth rates, we have:
- f2 (n log n)
- f3 (n√n)
- f1 (10n)
Thus, the correct order is f2, f3, f1, which corresponds to option 'D'.
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Community Answer
Consider the following three functions.f1 = 10nf2 = nlognf3 = n√...
On comparing power of these given functions : f1 has n in power. f2 has logn in power. f3 has √n in power. Hence, f2, f3, f1 is in increasing order. Note that you can take the log of each function then compare.
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Consider the following three functions.f1 = 10nf2 = nlognf3 = n√nWhich one of the following options arranges the functions in the increasing order of asymptotic growth rate?a)f3,f2,f1b)f2,f1,f3c)f1,f2,f3d)f2,f3,f1Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the following three functions.f1 = 10nf2 = nlognf3 = n√nWhich one of the following options arranges the functions in the increasing order of asymptotic growth rate?a)f3,f2,f1b)f2,f1,f3c)f1,f2,f3d)f2,f3,f1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following three functions.f1 = 10nf2 = nlognf3 = n√nWhich one of the following options arranges the functions in the increasing order of asymptotic growth rate?a)f3,f2,f1b)f2,f1,f3c)f1,f2,f3d)f2,f3,f1Correct answer is option 'D'. Can you explain this answer?.
Consider the following three functions.f1 = 10nf2 = nlognf3 = n√nWhich one of the following options arranges the functions in the increasing order of asymptotic growth rate?a)f3,f2,f1b)f2,f1,f3c)f1,f2,f3d)f2,f3,f1Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the following three functions.f1 = 10nf2 = nlognf3 = n√nWhich one of the following options arranges the functions in the increasing order of asymptotic growth rate?a)f3,f2,f1b)f2,f1,f3c)f1,f2,f3d)f2,f3,f1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following three functions.f1 = 10nf2 = nlognf3 = n√nWhich one of the following options arranges the functions in the increasing order of asymptotic growth rate?a)f3,f2,f1b)f2,f1,f3c)f1,f2,f3d)f2,f3,f1Correct answer is option 'D'. Can you explain this answer?.
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