# How do you find the limit of #(cos (2x))^(3/(x^2))# as x approaches 0?

To find the limit of ( (\cos(2x))^{3/(x^2)} ) as ( x ) approaches 0, you can use the property of the natural logarithm to rewrite the expression as ( e^{\frac{3\ln(\cos(2x))}{x^2}} ). Then, apply L'Hôpital's Rule by taking the derivative of the numerator and the derivative of the denominator, and then finding the limit as ( x ) approaches 0. The result will be ( e^{\frac{-12}{0}} ), which tends towards ( e^{-\infty} ). Thus, the limit is 0.

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The limit should be

But:

and:

The exponent

hope it is clear

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