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 fx) = O(g(x)) and then prove g(x) = 0({X). AX) = 2x + x - 7 and g(x) = x Step 1 For large x, 2x² + x 7 > 3x². Hence |f(x)| 2 1g(x) for large x. For large x, 2x² + x 7< 3x². Hence |f(x)| s 3g(x) for large x. For large x, x² 2 2x? + x – 7. Hence |f(x)| 2 3g(x) for large x. Step 2 For large x, x? S 2x² + x – 7. Hence, Ig(x)| S 1 |f(X)| for large x. For large x, x² S 2x² + x – 7. Hence, Įg(x)| s 1 |f(x)| for large x. Hence, f(x) = O(g(x)) and g(x) = O((X)). Step 3 Hence, f(x) = O(g(x)) and g(x) = O(f(x)). For large x, 2x²+ x 7s 3x². Hence |f(x)| S 3g(x) for large X.
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 fx) = O(g(x)) and then prove g(x) = 0({X). AX) = 2x + x - 7 and g(x) = x Step 1 For large x, 2x² + x 7 > 3x². Hence |f(x)| 2 1g(x) for large x. For large x, 2x² + x 7< 3x². Hence |f(x)| s 3g(x) for large x. For large x, x² 2 2x? + x – 7. Hence |f(x)| 2 3g(x) for large x. Step 2 For large x, x? S 2x² + x – 7. Hence, Ig(x)| S 1 |f(X)| for large x. For large x, x² S 2x² + x – 7. Hence, Įg(x)| s 1 |f(x)| for large x. Hence, f(x) = O(g(x)) and g(x) = O((X)). Step 3 Hence, f(x) = O(g(x)) and g(x) = O(f(x)). For large x, 2x²+ x 7s 3x². Hence |f(x)| S 3g(x) for large X.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
Related questions
Question
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
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 fx) = O(g(x)) and then prove g(x) = 0(Ax).
Ax) =
) = 2x2
+ x - 7 and g(x) = x²
Step 1
For large x, 2x² + x 7 2 3x².
Hence |f(x)| 2 1g(x) for large x.
For large x, 2x² + x 7< 3x?.
Hence |f(x)| s 3g(x) for large x.
For large x, x2z 2x2 + x – 7.
Hence |f(x)| 2 3g(x) for large x.
Step 2
For large x, x?S 2x² + x – 7.
Hence, Įg(x)| s 1 |f(X)| for large x.
For large x, x² s 2x² + X – 7.
Hence, [g(x)| < 1 |f(x)| for large x.
Step 3
Hence, f(x) = O(g(x)) and g(x) =
O(f(x)).
Hence, f(x) = O(g(x)) and g(x) =
O(f(x)).
For large x, 2x²+ x 7< 3x².
Hence |f(x)| < 3g(x) for large x.
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