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Question 3 (3.1) Use the definition of O(f) to show that n² is O(n² log n). (3.2) Is n²log n also O(n²)? Prove your answer. Question 4: Use the rules (and if necessary, the definition) for ordering E-classes to arrange the following in order from lowest to highest: lgn; (1,0001); 1gn²; (Ign)²; n³+4; 24n³+16n; n² +5n. Question 5: Let A have 5 elements and B have 4 elements. (5.1) How many everywhere defined functions are there from A to B?

Question 3 (3.1) Use the definition of O(f) to show that n² is O(n² log n). (3.2) Is n²log n also O(n²)? Prove your answer. Question 4: Use the rules (and if necessary, the definition) for ordering E-classes to arrange the following in order from lowest to highest: lgn; (1,0001); 1gn²; (Ign)²; n³+4; 24n³+16n; n² +5n. Question 5: Let A have 5 elements and B have 4 elements. (5.1) How many everywhere defined functions are there from A to B?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 3 (3.1) Use the definition of O(f) to show that n² is O(n²log n). (3.2) Is n²log n also O(n²)? Prove your answer. Question 4: Use the rules (and if necessary, the definition) for ordering e-classes to arrange the following in order from lowest to highest: lgn; (1,0001); Ign²; (Ign)²; n³+4; 24n³ +16n; n²+5n. Question 5: Let A have 5 elements and B have 4 elements. (5.1) How many everywhere defined functions are there from A to B? (5.2) How many everywhere defined one-to-one functions are there from A to B? Explain your answer.
Transcribed Image Text:Question 3 (3.1) Use the definition of O(f) to show that n² is O(n²log n). (3.2) Is n²log n also O(n²)? Prove your answer. Question 4: Use the rules (and if necessary, the definition) for ordering e-classes to arrange the following in order from lowest to highest: lgn; (1,0001); Ign²; (Ign)²; n³+4; 24n³ +16n; n²+5n. Question 5: Let A have 5 elements and B have 4 elements. (5.1) How many everywhere defined functions are there from A to B? (5.2) How many everywhere defined one-to-one functions are there from A to B? Explain your answer.
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