Limit of Function w/ 0<q<1: Solved by Bincy

[bincy]

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]

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

 

[bincy]

Thanks a ton (Bow)(Bow)