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Lim x-->a- ( |x| 3 /a – [x/a] 3 ) a please solve the above question. I've tried sandwich theorem but couldn't get the answer. Please provide the solution

Limx-->a- (|x|3/a – [x/a]3 ) a
please solve the above question. I've tried sandwich theorem but couldn't get the answer. Please provide the solution

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1 Answers

Aditya Gupta
2081 Points
4 years ago
the limit splits as
lim|x|3 – lim a*[x/a]3 
|a|^3 – a*0^3 (as x tends to a from LHS, so x/a tends to 1 from LHS, causing the gif to equal zero)
=|a|^3  [note that this is the answer if [.] represents the GIF]
if [.] does not represent the GIF, then the answer is straightaway
|a|^3 –a*1^3
=|a|^3 –a

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