Solving lim(x->0)((cosx)^(-4/(x^2))) without L'Hopital's Rule lim(x->0)((cosx)^(-4/(x^2))) I would like to know how I can solve it without using De L'Hospital's rule....

Solving lim(x->0)((cosx)^(-4/(x^2))) without L'Hopital's Rule

lim(x->0)((cosx)^(-4/(x^2)))

I would like to know how I can solve it without using De L'Hospital's rule.

http://img803.imageshack.us/img803/7954/wolframalphalimxgt0cosx.png

Thanks!

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You need to take logarithm of the limit such that:

`ln lim_(x->0) ((cosx)^(-4/(x^2))) => lim_(x->0) ln ((cosx)^(-4/(x^2)))`

You need to use the logarithmic identity such that:

`lim_(x->0) -4/(x^2) ln (cos x) = -oo/oo`

You may use l'Hospital's theorem such that:

`lim_(x->0)...

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