Determine the area between the curves \( y = x^2 \) and \( y = 4 - x^2 \) for the interval where they intersect.

Identify the horizontal asymptote of the function \( f(x) = 3 e^{-x} + 5 \).

12. The position of a particle is given by the equation \( x(t)=5 t^{3}-2 t^{2} \). How much does the particle's velocity change from \( t=1 \) second to \( t=3 \) seconds?

If a car has an acceleration function of \( a(t) = 6t \), what is its velocity function assuming it starts from rest?

\( \int \frac { \sqrt { x ^ { 2 } - 2 x } } { x } d x = \)

(c) \( \lim _{x \rightarrow+\infty} \frac{\sqrt{x}}{\sqrt{x+\sqrt{x+\sqrt{x}}}} \)