4.2 \( 1 \leqslant \quad \begin{array}{l}\text { A marshy region used for agricultural drainage has become contaminated with a particular element. It has been determined that flushing the area with clean water will reduce the } \\ \text { element for a while, but it will then begin to build up again. A biologist has found that the percent of the element in the soil } x \text { months after the flushing begins is given by the function } \\ \text { below. When will the element be reduced to a minimum? What is the minimum percent? } \\ f(x)=\frac{x^{2}+16}{2 y}, 1 \leq x \leq 12\end{array} \)

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

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

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

The cost to produce \( x \) items is modeled by \( C(x)=0.003 x^{2}+3.2 x+60 \) dollars and the revenue from selling \( x \) items is given by \( R(x)=6 x \) dollars. a. Find the marginal profit when 359 items are sold using the formula \( P(x+1)-P(x) \). (Round your answer to three decimal places.) b. Use the derivative to estimate the marginal profit when 359 items are sold. (Round your answer to three decimal places.)

Al calcular el \( \lim _{x \rightarrow 0} \frac{\sin 4 x}{\tan x} \) se obtiene: a. 0 b. 4 c. \( 1 / 4 \) d. No existe