# A limit problem

#### oahsen

1. Homework Statement
f(x)=(tan(x)/x)^(1/(x^2)) it asks the limit of this function when x goes to 0

2. Homework Equations

3. The Attempt at a Solution

i have tried to take the ln of the two sides than used the l'hopital rule but with that way i could not reach anything. pls help me

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#### StatusX

Homework Helper
What exactly went wrong when you tried that?

#### marlon

Develop the tan(x) in a series first. Using the actual tan(x) always gives me infinity divided by zero.

The Taylor series of tan(x) around zero is valid for |x| < pi/2 so...

marlon

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#### dextercioby

Homework Helper
If the limit is NOT 0, then Marlon's suggested method leads to an erroneous result.

Daniel.

#### marlon

If the limit is NOT 0, then Marlon's suggested method leads to an erroneous result.

Daniel.
Actually, YES, you are right. Actually, i don't know how to solve it so i am gonna say it's indefinite :rofl:

marlon

#### dextercioby

Homework Helper
I get infinity, plus or minus, depending on whether the limit is approaching 0 from below or from above.

Daniel.

#### marlon

I get infinity, plus or minus, depending on whether the limit is approaching 0 from below or from above.

Daniel.
Yeah, (1+x^2)^(1/x^2) for x--> 0 (after doing the Taylor thing) gives me this : 1 + x > 1 and the power gets bigger if x gets towards 0, so you are EVOLVING towards infinity but what i cannot achieve is prove that the value is actually infinite

Also, if x is coming from te negative side, you are again evolving toward positive infinity because tanx/x = 1 + (x^2)/3 + ... with all positive powers !!!

marlon

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