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Give a big-O estimate for each of these functions. For the function g in your estimate f(x) is Og(x)), use a simple function g of smallest order. If f(x) = (n³ + n² log n)(log n + 1) + (17 log n+19)( n³ + 2), then g(x) = Multiple Choice 13 O n-log n log n log n

Give a big-O estimate for each of these functions. For the function g in your estimate f(x) is Og(x)), use a simple function g of smallest order. If f(x) = (n³ + n² log n)(log n + 1) + (17 log n+19)( n³ + 2), then g(x) = Multiple Choice 13 O n-log n log n log n

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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Please help me with these two questions. I am having trouble understanding what to do.

 

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NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Give a big-O estimate for each of these functions. For the function g in your estimate f(x) is O(g(x)), use a simple function g of smallest order. If f(x) = (n³ + m² log n)(log n + 1) + (17 log n+19)( n³ + 2), then g(x) = ________ Multiple Choice 13 n-log n log n log n
Transcribed Image Text:NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Give a big-O estimate for each of these functions. For the function g in your estimate f(x) is O(g(x)), use a simple function g of smallest order. If f(x) = (n³ + m² log n)(log n + 1) + (17 log n+19)( n³ + 2), then g(x) = ________ Multiple Choice 13 n-log n log n log n
Click and drag the steps to their corresponding step numbers to prove that the given pair of functions are of the same order. (Note: Consider to prove the result, first prove f(x) = O(g(x)) and then prove g(x) = O(f(x)). f(x) = 2x²+x-7 and g(x) = x² Step 1 Hence, f(x) = O(g(x)) and g(x) = O(f(x)). Step 2 For large x, 2x² + x 7 ≥ 3x². Hence |f(x)|≥1g(x) for large x. For large x, x² ≤ 2x²+x-7. Hence, g(x) ≤ 1 |f(x)| for large x. Step 3 For large x, x² ≥ 2x²+x-7. Hence |f(x)|≥ 3g(x) for large x. For large x, 2x² + x 7 ≤ 3x². Hence |f(x)| ≤ 3g(x) for large x.
Transcribed Image Text:Click and drag the steps to their corresponding step numbers to prove that the given pair of functions are of the same order. (Note: Consider to prove the result, first prove f(x) = O(g(x)) and then prove g(x) = O(f(x)). f(x) = 2x²+x-7 and g(x) = x² Step 1 Hence, f(x) = O(g(x)) and g(x) = O(f(x)). Step 2 For large x, 2x² + x 7 ≥ 3x². Hence |f(x)|≥1g(x) for large x. For large x, x² ≤ 2x²+x-7. Hence, g(x) ≤ 1 |f(x)| for large x. Step 3 For large x, x² ≥ 2x²+x-7. Hence |f(x)|≥ 3g(x) for large x. For large x, 2x² + x 7 ≤ 3x². Hence |f(x)| ≤ 3g(x) for large x.
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