Limit of x*cot(x)-1/x^2 as x->0

[tsuwal]

Homework Statement

limit x*cot(x)-1/x^2
x->0

Homework Equations

lim x*cot(x)=1
x->0

The Attempt at a Solution

it's an indetermination but L'hopital rule doesn't help very much..

 

[Dick]

Homework Statement

limit x*cot(x)-1/x^2
x->0

Homework Equations

lim x*cot(x)=1
x->0

The Attempt at a Solution

it's an indetermination but L'hopital rule doesn't help very much..

Sometimes l'Hopital works better if you try rearranging things. Substitute cot(x)=cos(x)/sin(x). Multiply numerator and denominator by sin(x) and try again.

 

[haruspex]

limit x*cot(x)-1/x^2
x->0

I assume you mean limit (x*cot(x)-1)/x² as x->0.
The indeterminacy simply means you've not gone far enough in the expansion of the functions as power series. What expansions do you know for tan x, or failing that, for sin x and cos x?

 

[tsuwal]

thanks Dick, i wish i could see the those simplifications right away!