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\[ \displaystyle \int_{0}^1 \int_0^1 1 + \dfrac{xy}{2 + \dfrac{xy}{2+ \dfrac{xy}{2+ \cdots}}} \, dy \, dx \]

If the answer can be represented in the form ...

Let \( S \) be the set containing all the points in the image of \( f(x) = \dfrac{\arctan x + \text{arccot} x}{\sqrt{\arctan^2 x + \text{arccot}^2 x}} \). Compute ...

Suppose you have a triangle ABC, with \( A = (0, 0), B = (1, 3), C = (3, 1) \). Point P lies on \( \overline{AC} \), such that the area of triangle APB equals ...

\[ \displaystyle \lim_{x \to 0} \dfrac{x^2 \left( \left[ 4 \sin x - 3 \cos x + \dfrac{5}{2} \arcsin^2 (\arctan x) + 4\right]^{2017} -1 \right) }{\tan (2017x)(1 - \cos(\sin x))} \]

\[\large \lim_{x \to 0} \dfrac{(1-\cos x)^{58} }{\ln^{116}(2x + 3 - 2 \cos x) } \]

If the above limit equals \( L \), compute \( \log_2 L \).

Hint: The problem is ...

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