Determine the following limits: 1.1.1 \( \lim _{x \rightarrow \infty} \frac{\ln \left(1+e^{x}\right)}{5 x} \) 1.1.2 \( \quad \lim _{x \rightarrow 0} \frac{3^{x}-2^{x}}{x^{2}-x} \)

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

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.)

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.

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.

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.