Evaluate: `("lim")_(x->7/2)(2x^2-9x+8)^(cot(2x-7))`

Options

A. both `underset(xtoa)limf(x)` and `underset(xtoa)limg(x)` must exist
B. `underset(xtoa)limf(x)` need not exist but `underset(xtoa)limg(x)` exists
C. neither `underset(xtoa)limf(x)` nor `underset(xtoa)limg(x)` may exist
D. `underset(xtoa)limf(x)` exists but `underset(xtoa)limg(x)` need not exist

Explanation

To evaluate the limit

\[ L = \lim_{x \to \frac{7}{2}} \left(2x^2 - 9x + 8\right)^{\cot(2x - 7)}, \]

we will proceed step by step.

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