Evaluate the following limit: `(lim)_(x->0)(1-cos5x)/(1-cos6x)`

Explanation

To evaluate the limit

\[ L = \lim_{x \to 0} \frac{1 - \cos(5x)}{1 - \cos(6x)}, \]

we first observe that substituting \(x = 0\) directly gives us the indeterminate form \(\frac{0}{0}\). Therefore, we can apply L'Hôpital's Rule, which states that if we have an indeterminate form, we can differentiate the numerator and the denominator separately.

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