Unformatted text preview: equations in Q2. Q4. Prove that { 1 , log(1 + Ç« ) , log(1 + Ç« 2 ) , log(1 + Ç« 3 ) , . . . } is an asymptotic sequence as Ç« â†’ 0. Q5. Arrange the following so that they form an asymptotic sequence as Ç« â†’ 1 , Ç« 1 2 , Ç« 2 , log 1 Ç« , Ç« 1 2 , Ç« 2 log 1 Ç« , log(log 1 Ç« ) , Ç« 3 2 , Ç« 1 2 log 1 Ç« . ( Hint: log 1 Ç« = o ( 1 Ç« p ) as Ç« â†’ 0 for any p > 0)...
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 Spring '09
 SARKAR
 Math, asymptotic sequence, Obtain twoterm expansions, perturbation series solutions

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