# Lim (1/x)^tan(x) as x->0 ? help please..

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1. Nov 27, 2015

### felipe oteiza

l'hopital must be apply, i'll be very grateful

2. Nov 27, 2015

### BvU

Hello felipe

Do you know the limit for $\sin x \over x$ ?

3. Nov 27, 2015

### BvU

oops, sorry, you mean $$x^{-\tan x}\ \ ?$$

4. Nov 27, 2015

### felipe oteiza

yes! the last

5. Nov 27, 2015

### BvU

Where does $\ x^{\tan x}\$ go for $\ x\downarrow 0$ ?

6. Nov 27, 2015

### felipe oteiza

lim ( 1/x )^tan x as x->0

7. Nov 27, 2015

### BvU

Yes, that was my question

8. Nov 27, 2015

### felipe oteiza

I dont understand your question (my english is not very good)

9. Nov 27, 2015

### BvU

What is the limit $\ \ \displaystyle \lim_{x\downarrow 0} \ x^{\tan x}\$ ?

10. Nov 27, 2015

### mathman

tanx ~ x as x ->0, so problem can be looked at as $\lim_{x-->0} x^x$ However $x^x=e^{xlnx}$.
Since $\lim_{x->0}xlnx=0$, the final answer = 1.

11. Nov 27, 2015

### felipe oteiza

thanks

12. Nov 28, 2015

### shaztp

Tan (0)=0 there for answer will be 1

13. Nov 28, 2015

### mathman

Not by itself. The function is $(\frac{1}{x})^{tanx}$, so as x->0, the expression becomes $(\frac{1}{0})^{0}$ which is indeterminate.