Suppose an object moves along a line at \( 16 \mathrm{~m} / \mathrm{s} \) for \( 0 \leq \mathrm{t} \leq 3 \mathrm{~s} \) and at \( 26 \mathrm{~m} / \mathrm{s} \) for \( 3<t \leq 5 \mathrm{~s} \). Sketch the graph of the velocity function and find the displacement of the object for \( 0 \leq \mathrm{t} \leq 5 \) the displacement of the object for \( 0 \leq 1 \leq 5 \) is

\( : \int _ { - 3 } ( x ^ { 2 } + 7 x - 8 ) d x \)

2) La ecuación del movimiento de una particula está dada por: \( s(t)=t^{3}-3 t \) Encontrar: a) La velocidad como función de \( t \) b) La aceleración después de 4 segundos. c) la aceleración cuando la velocidad es cero.

Use a Riemann sum to approximate the area under the graph of \( f(x)=4 e^{-x} \) on the interval \( 0 \leq x \leq 1 \) using \( n=5 \) subintervals with the selected points as the right end points. The area is approximately \( \square \) units. (Round to six decimal places as needed.)

1. \( y=\frac{x}{\sqrt[4]{25-x^{2}}} \)

Find the average rate of change of \( h(x)=-2 x^{2}-5 x \) from \( x=-4 \) to \( x=1 \). Simplify your answer as much as possible.