Let's solve the limit of secant x to the power of cotangent x as x approaches pi over 2. As x approaches pi over 2, secant x approaches infinity and cotangent x approaches zero, creating the indeterminate form infinity to the power of zero. Looking at values approaching pi over 2, we can see this behavior clearly. We need logarithmic techniques to solve such limits.
The key technique is logarithmic transformation. If y equals secant x to the power of cotangent x, then natural log of y equals cotangent x times natural log of secant x. We transform the original limit to the limit of natural log of secant x to the power of cotangent x, which equals the limit of cotangent x times natural log of secant x. This creates a new indeterminate form zero times infinity, which can be converted to zero over zero or infinity over infinity form for L'Hôpital's rule application.