# Limit of a function

#### bincybn

##### Member
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
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

Thanks a ton