\( \sum _ { n = 2 } ^ { \infty } \frac { \log ( ( 1 + \frac { 1 } { n } ) ^ { n } ( 1 + n ) ) } { ( \log n ^ { n } ) ( \log ( n + 1 ) ^ { n + 1 } ) } : \log _ { 2 } \sqrt { e } \)

Al calcular el \( \lim _{x \mapsto \frac{\Pi}{4}} \frac{\cos x-\sin x}{\cos ^{2} x} \) se obtiene: \( \begin{array}{l}\text { a. } \sqrt{2} \\ \text { b. } 1 \\ \text { c. } 2 / \sqrt{2} \\ \text { d. } \sqrt{2} / 2\end{array} \).

\( \left. \begin{array} { l } { \operatorname { si } F ( x ) = \frac { 2 x ^ { 2 } + 3 x } { x \rightarrow 3 } } \\ { \lim _ { x \rightarrow - 2 } } \end{array} \right. \)

Use polynomial long division to evaluate the integral of \( \frac{x^4 + 6x^3 + 4x^2 + 8}{x^2 + 2} \) for integration.

\( \lim _ { x \rightarrow \infty } \frac { e ^ { x } \cdot \operatorname { ch } ( 2 x ) } { 1 h ( 3 x ) } \)

Al calcular el \( \lim _{x \rightarrow 0} \frac{1-\cos x}{\sin x} \) se obtiene: a. 0 b. No existe c. -1 d. 1