Exercise 1.3 1. Determine which of the following statements are true and which are false. a) \( \{ \) Abraham, Azieb \( \} \subset\{ \) Ali, Abraham, Azieb \( \} \) Yes b) \( \{x: x \) is a prime number \( \} \subset\{x: x \) is an odd integer \( \} \) c) \( \{x: x \) is a prime number \( \} \subset\{x: x \) is a rational number \( \} \) Let \( N= \) The set of natural numbers \( \mathrm{Z}= \) The set of integers

6 Let \( f(x)=-1.215 x^{3}+2.31 x^{2}+5.2 x+3.1 \) where \( -3 \leq x \leq 3 \). a) The function \( f \) has a relative minimum at \( x= \) b) The function \( f \) has a relative maximum at \( x= \) c) On what interval(s) is \( f \) increasing? d) On what interval(s) is \( f \) decreasing?

Hallar las derivadas sucesivas de: \( f(x)=3 x^{4}+5 x^{2}+2 x-5 \)

Find all solutions to the equation in the interval \( (0,2 \pi) \) \( \cos \frac{x}{2}=-\frac{\sqrt{3}}{2} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \{ \) ? \( \} \). There is no solution.

A 14.0 kg bucket is pulled up a well by a rope at a constant speed on Earth. What is the force of weight on the bucket?

\( \begin{array}{lc}\text { 6. A partir de los siguientes datos: } & \\ \mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g}) & \Delta \mathrm{H}=-393,5 \mathrm{KJ} / \mathrm{mol} \\ \mathrm{H}_{2}(\mathrm{~s})+y_{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{I}) & \Delta \mathrm{H}=-285,8 \mathrm{KJ} / \mathrm{mol} \\ 2 \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})+7 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 4 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{I}) & \Delta \mathrm{H}=-3119,6 \mathrm{KJ} / \mathrm{mol} \\ \text { Calcule el cambio de entalpía para la reacción: } & \\ 2 \mathrm{C}(\mathrm{s})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g}) & \end{array} \)