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

Evaluate the function. If the value is not a rational number, round your answer to three decimal places. (a) \( \operatorname{csch}^{-1}(3) \) (b) \( \operatorname{coth}^{-1}(6) \)

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

Suppose that the function \( f \) is defined for all real numbers as follows. \[ f(x)=\left\{\begin{array}{ccc}6 & \text { if } & x<-4 \\ -10+x^{2} & \text { if } & -4 \leq x<4 \\ 2 x-2 & \text { if } & x \geq 4\end{array}\right. \] Graph the function \( f \). Then determine whether or not the function is continuous.

An equation for the slant asymptote for the graph of the function \( f(x)=\frac{2 x^{2}-x+3}{x+4} \) is

\( f(x)=\frac{12 x}{7 x^{2}+9} \) 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.