1. \( \left(4 x^{2}+3 y^{5}\right)(2 x \) 2. \( (3 x-2 y)(9 x \) 3. \( 2 x(3 x-4 y)-1 \) 4. \( (2 x+y)^{2}-(3 x \) 5. \( x^{6}+\left(x^{3}-3 y\right. \)

Centro 2 - El cuartel - Ejercitación A) Ejercicios contextualizados 1) En el cuartel, la mitad del espacio está ocupada por los camiones de bomberos, \( \frac{1}{6} \) del espacio está ocupado por la cocina, \( \frac{1}{4} \) del espacio está ocupado por el dormitorio y el cuarto de lavandería ocupa resto del espacio. ¿Qué fracción corresponde al espacio del cuartel que está ocupado por el cuarto de lavanderia?

Ch. 8: Limits and Continuity EXAMPLE 17 .

A ball is thrown vertically upward from the top of a building 128 feet tall with an initial velocity of 32 feet per second. The distance \( s \) (in feet) of the ball from the ground after \( t \) seconds is \( s(t)=128+32 t-16 t^{2} \). (a) After how many seconds does the ball strike the ground? (b) After how many seconds will the ball pass the top of the building on its way down? (a) After \( \square \) seconds the ball strikes the ground. (b) The ball passes the top of the building on its way down after seconds.

For the following function \( \frac{\mathrm{us}}{\mathrm{dt}} \), find the antiderivative \( s \) that satisfies the given condition. \[ \frac{\mathrm{ds}}{\mathrm{dt}}=2 \sin 2 \mathrm{t}-16 \cos 16 \mathrm{t} ; \mathrm{s}\left(\frac{\pi}{4}\right)=6 \] The antiderivative that satisfies the given condition is \( s(t)=\square \).

Simplify the expression. \[ (-5)^{2}+4^{3} \]