126. Los têrminos de una sucesón se calculan con este procedimiento. Paso 1. El primer término de la sucesión es \( f^{\prime}(1)=1 \) Paso 2: El término de la posición n se calcula usando el término de la posición n-1, por medio de la formula: \( f(n)=1+\frac{1}{\Gamma(n-1)} \) Por ejemplo: \[ \begin{array}{c} f(2)=1+\frac{1}{f(1)} \\ f(2)=1+\frac{1}{1} \\ f(2)=2 \end{array} \] ¿Cual es el valor de \( f(3) \) ? A. \( \frac{1}{2} \) B. \( \frac{3}{2} \) C \( \frac{1}{2} \) D. \( \frac{2}{3} \)

servers at locations \( x, y \), and \( z \). The total number of servers is constrained by \( x+y+z=20 \). Find the configuration of servers that minimizes latency. 2. The network latency \( L(x)=-2 x^{2}+12 x-10 \) for data packets is studied for input size ' \( x \) '. If the latency is equal at \( x=1 \) and \( x=5 \), use Rolle's theorem to find a value ' \( c \) ' in the interval \( (1,5) \) where the latency's rate of change is zero.

Find the value of \( x \) at which the series converg and give the sum : \( \begin{array}{ll}\text { (a) } \sum_{n=1}^{\infty} n^{-3 x} & \text { (b) } \sum_{n=1}^{\infty}(\ln x)^{n}\end{array} \)

10. A company manufactures and sales \( X \) units of DSTV per month. If the monthly cost \[ C(X)=10,000+4 x \] \[ P(X)=20-\frac{X}{2,000} \text { P is price }[0,4000] \] For each month find:- 1) The production level that leads to maximum revenue and the maximum revenue. 2) The production levels that leads to maximum profit and the maximum profit. 3) The production level that leads to minimum cost and the minimum cost.

\( ( 4 x + 2 y ) d x + ( 2 x - 4 y ) d y = 0 \)

A área transversal de um solide varia conforme é exato \( A(x) = 2x + 1 \). Encontre o volume desse sólido sobre o intervalo \([0, 4]\).