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grows much faster than al olem, you will improve on above. rds, define six sequences {- all c> 1: < ®n << n° << wn <<

grows much faster than al olem, you will improve on above. rds, define six sequences {- all c> 1: < ®n << n° << wn <<

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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(5) The Big Theorem describes the relative growth rates of five different types of sequences that all diverge to o. It says that for all a > 0 and all c> 1: In n << n° << c"<< n! << n". That means, for example, that all sequences of the form {nª} grow much faster than {In n}, and that {n!} grows much faster than all sequences of the form {c"}. In this problem, you will improve on The Big Theorem by "filling in" the six gaps left by the statement above. In other words, define six sequences {un}, {Un}, {Wn}, {rn}, {Yn}, and {zn}, such that, for all a > 0 and all c > 1: Un << Inn << vn << n° << wn << c" <<< *n << n! << Yn << n" << zn The final draft of your solution that you submit should be structured as follows: At the top, a clear list of your six sequences, named the same way as above. Below that, a justification of all 10 of the "<<" relationships that you are claiming.
Transcribed Image Text:(5) The Big Theorem describes the relative growth rates of five different types of sequences that all diverge to o. It says that for all a > 0 and all c> 1: In n << n° << c"<< n! << n". That means, for example, that all sequences of the form {nª} grow much faster than {In n}, and that {n!} grows much faster than all sequences of the form {c"}. In this problem, you will improve on The Big Theorem by "filling in" the six gaps left by the statement above. In other words, define six sequences {un}, {Un}, {Wn}, {rn}, {Yn}, and {zn}, such that, for all a > 0 and all c > 1: Un << Inn << vn << n° << wn << c" <<< *n << n! << Yn << n" << zn The final draft of your solution that you submit should be structured as follows: At the top, a clear list of your six sequences, named the same way as above. Below that, a justification of all 10 of the "<<" relationships that you are claiming.
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