Elegir la opción que contiene la transformada de Laplace de la siguiente fur \[ f(t)=\cos ^{2} 2 t \] Seleccione una: a. \( \frac{s^{2}+2}{s\left(s^{2}+4\right)} \) b. \( \frac{s^{2}+8}{s\left(s^{2}+16\right)} \) c. \( \frac{1}{s}+\frac{s}{s^{2}+16} \) d. \( \frac{1}{s}+\frac{s}{s^{2}+4} \)

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

9. The market research department of a Company recommends that the Company to manufacture and market new TV after suitable test. The marketing department also presents the following demand equation. \( X=28,000-2000 P \) or \( P=14-x / 2000 \), where \( P \) is price and \( X \) is production. Furthermore, the financial department provides the following cost equation: \( C(X)=15 \), \[ 000+7 x \] Conduct a marginal analysis for the company and calculate the amount of the products that maximized total profit?

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.

If time \( t \) be regarded as a function of velocity \( v \), prove that the rate decrease of acceleration \( f \) is given by \( f^{\frac{d}{} f^{\prime}} d v^{2} \) [Bikaner सस्न रेखा में चल रहे किसी कण की मूल बिंद ती दूरी \( x \) पर वेग \( \left.\left(a^{2}-x^{2}\right)^{\frac{1}{2}} \right\rvert\, x^{2} \) सम्यनुपाती है। इसके त्वरण का नियम ज्ञात कीजिए। The velocity of a particle moving along a straight line, when a distance \( x \) from the origin varies as \( \left(a^{2}-x^{2}\right)^{\frac{1}{2}} / x^{2} \). Find the law

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.