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Limit of a function

bincybn

Member
Apr 29, 2012
36
Hello,

\(\displaystyle \underset{n\rightarrow\infty}{Lt} \frac{n^{(1+q)}}{e^{(\frac{1}{2})n^{(1-q)}}}
\)

where\(\displaystyle 0<q<1\)



I tried using L' Hospitals rule but could not able to do since same pattern was repeating. I strongly believe that the limit is 0.


regards,
Bincy
 

CaptainBlack

Well-known member
Jan 26, 2012
890
Hello,

\(\displaystyle \underset{n\rightarrow\infty}{Lt} \frac{n^{(1+q)}}{e^{(\frac{1}{2})n^{(1-q)}}}
\)

where\(\displaystyle 0<q<1\)



I tried using L' Hospitals rule but could not able to do since same pattern was repeating. I strongly believe that the limit is 0.


regards,
Bincy

Try putting \(u=\frac{1}{2}n^{1-q}\), and remember that \[\lim_{x \to \infty} \frac{x^k}{e^x}
=0\] for all real \(k\)

CB
 

bincybn

Member
Apr 29, 2012
36
Thanks a ton (Bow)(Bow)