Matematické Fórum

stuart clark · 21. 04. 2016 07:22

Evaluation of $\lim_{x\rightarrow 0}\bigg\lfloor \frac{x^2}{\sin x\tan x}\bigg\rfloor$ and $\lim_{x\rightarrow 0}\bigg\lfloor \frac{\sin x\tan x}{x^2} \bigg\rfloor$ .

Where $\lfloor x \rfloor$ Represent floor function of $x$ .

Marian · 13. 05. 2016 10:55

↑ stuart clark:

Let $0<|x|\le\tfrac{\pi}{4}$ . Then

Hence, we obtain

For the second limit, we procced analogously. For all $x$ under consideration we have

Hence,

To prove the stated inequalities, one can use standard techniques. (I omit the details.)

stuart clark · 01. 06. 2016 05:02

Thanks ↑ Marian:, We can also solved it Using Arithmetic- Inequality.

Matematické Fórum

#1 21. 04. 2016 07:22

2 Limits

#2 13. 05. 2016 10:55

Re: 2 Limits

#3 13. 05. 2016 21:53 Příspěvek uživatele Pritt byl skryt uživatelem Pritt. Důvod: mistakes were made...

#4 01. 06. 2016 05:02

Re: 2 Limits

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