Thursday, 13 March 2014

Calculate limit for the following function



I want to calculate the limit for the following function.




$$\lim_{n\to+\infty} \frac{(3/2)^n}{(\log n)^{\log n}}$$



I have tried it using L'Hospital use but the result of differentiation is much more complicated.


Answer



Hint:
$$
\frac{(3/2)^x}{(\log x)^{\log x}}=e^{x\log(1.5)-\log(x)\log\log(x)}
$$


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