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Let IER be an interval with Oel, let pen and let g:l\{0}→R be a function with g(x) = O(|x|³) as x → 0.

Let IER be an interval with Oel, let pen and let g:l\{0}→R be a function with g(x) = O(|x|³) as x → 0.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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Which of the following statements are correct?

 

Let IER be an interval with OЄl, let pen and let g:l\{0}→r be a function with g(x) = O(|x|P) as x → 0.
Transcribed Image Text:Let IER be an interval with OЄl, let pen and let g:l\{0}→r be a function with g(x) = O(|x|P) as x → 0.
g(x)/x=0(|x|P-¹) as x→0. a. If p≥1, then b. We have -g(x)=O(|x|º) as x→0. c. We have xg(x)=0(|×|p+¹) as x→0. Od. For any c>0, we have cg(x)=0(|x|P) as x→0.
Transcribed Image Text:g(x)/x=0(|x|P-¹) as x→0. a. If p≥1, then b. We have -g(x)=O(|x|º) as x→0. c. We have xg(x)=0(|×|p+¹) as x→0. Od. For any c>0, we have cg(x)=0(|x|P) as x→0.
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