How do you know if a number is in scientific notation? How can you tell if a number in scientific notation has a large or small value?

1) If \( y=\sqrt{n^{3}}, x=2 n^{2}+7 \), then \( \frac{d y}{d x}=\cdots \) when \( n=1 \) \( \begin{array}{llll}\text { a) } \frac{3}{8} & \text { b) } \frac{3}{4} & \text { c) } 2 & \text { d) } 6\end{array} \)

Deriva la función \( f(x)=x^{4} \) mediante el uso del límite

b) Graficar una función \( g \) tal que \( g(3)=2 \) y \( g^{\prime}(3)=0 \).

The table to the right shows the digits of the octal system (base eight) and their equivalents in the binary system (base two). Use the table to fill in the blanks below. (a) Write \( 613_{\text {eight }} \) in the binary system. (b) Write \( 1110101011_{\text {two }} \) in the octal system. \( 1110101011_{\text {two }}=\square_{\text {eight }} \)

If \( 4 \tan \theta=3 \) and \( 180^{\circ}<\theta<360^{\circ} \), determine with the aid of a diagram: \( \begin{array}{ll}5.1 .1 \cos \left(180^{\circ}+\theta\right) & \text { (4) } 1 \\ 5.1 .2 \tan 2 \theta & \text { (3) } 1 \\ 5.1 .3 \sin \left(45^{\circ}+\theta\right) & \text { (4) } 1\end{array} \)