(3,0 punto) Determine los valores de \( c \in \mathbb{R} \), usando solo propiedades de stumatorias, para que sc cumpla la siguientc igualdad: \[ \sum_{k=2}^{7}\left(\frac{c^{2}}{139}-\frac{k}{9 c}\right)=\sum_{k=12}^{39}(\sqrt{2 k+1}-\sqrt{2 k+3}) \]

Use the value of the given hyperbolic function to find the values of the other hyperbolic functions. \( \sinh (x)=\frac{5}{4} \) \( \tanh (x)= \) \( \operatorname{csch}(x)= \) \( \operatorname{sech}(x)= \) \( \operatorname{coth}(x)= \)

Evaluate the function. If the value is not a rational number, round your answer to three decimal places. (a) \( \sinh (1)=\square \) (b) \( \tanh (-8)=\square \)

Evaluate the function. If the value is not a rational number, round your answer to three decimal places. (a) \( \operatorname{csch}(\ln (4)) \) (b) \( \operatorname{coth}(\ln (6)) \)

Find any vertical asymptotes. \( h(x)=\frac{(x-3)(x+6)}{x^{2}-4} \)

\( f(x)=\frac{12 x}{7 x^{2}+9} \) Find the horizontal asymptote, if any, of the graph of the rational function. A. The horizontal asymptote is \( \square \). (Type an equation.) B. There is no horizontal asymptote.