A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field into 3 identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.

\( \lim _ { x \rightarrow \infty } ( \frac { 3 x + 1 } { 3 x - 5 } ) ^ { \frac { 3 x ^ { 5 } + 4 x - 3 } { ( 2 x - 1 ) ^ { 2 } ( x + 2 ) ^ { 2 } } } \)

9.- Calcula la derivada de la función * \( y=\left(x^{2}+b^{2}\right)^{4} \) \( \begin{array}{ll}\text { A) } \frac{d y}{d x} 8 x\left(x^{2}+b^{2}\right)^{5} & \text { B) } \frac{d y}{d x} 8 x^{2}\left(x^{2}+b\right)^{3} \\ \text { C) } \frac{d y}{d x} 8 x\left(x^{2}+b^{2}\right)^{3} & \text { D) } \frac{d y}{d x} 8\left(x^{2}+b^{2}\right)^{3}\end{array} \)

\( \int \frac { 3 / \sqrt { a ^ { 3 } y ^ { 4 } } x d x } { 4 / 3 a ^ { 2 } b ^ { 3 } x ^ { 2 } + 6 } \)

1) \( \int_{8}^{\frac{\text { III }}{\frac{\pi}{2}}} x \cdot c \)

Find \( (A) f^{\prime}(x) \), (B) the partition numbers for \( f^{\prime} \), and \( (C) \) the critical numbers of \( f \). \( f(x)=x^{3}-12 x-8 \) (A) \( f^{\prime}(x)=\square \) (B) Find the partition numbers for \( f^{\prime} \). Select the correct choice below and, if necessary, fill in the answer box to complete your choic A. The partition pumber(s) is/are \( x=\square \). (Use a comma to separate answers as needed.) B. There are no partition numbers. (C) Find the critical numbers for \( f \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical number(s) is/are \( x=\square \). (Use a comma to separate answers as needed.)