solve this---**Question Stem:** Evaluate the following limit: `lim (x→π/2) (sec x)^(cot x)` **Mathematical Formulas:** The problem asks to evaluate the limit: `lim_{x→π/2} (sec x)^{cot x}`

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Let's evaluate the limit of secant x to the power of cotangent x as x approaches pi over 2. First, we need to identify what type of limit this is. As x approaches pi over 2, secant x approaches infinity, while cotangent x approaches zero. This creates an indeterminate form of infinity to the power of zero. To solve this type of exponential limit, we'll use a logarithmic transformation strategy. Now we'll apply the logarithmic transformation technique. Let y equal secant x to the power of cotangent x. Taking the natural logarithm of both sides, we get ln y equals cotangent x times ln of secant x. This allows us to take the limit of ln y instead of y directly. The limit becomes the limit of cotangent x times ln secant x as x approaches pi over 2. This transformation converts our indeterminate form from infinity to the power of zero into zero times infinity, which we can handle more easily.