dériver: \( (3-x) e^{x}+1 \)

(4) show that \( \lim _{z \rightarrow a} \) \( \frac{i z^{3}+i z-1}{2 z+3 i(z-i)} \)

Compute the average value of \( f(t) = \sin(t) + \cos(t) \) over the interval \([0, \pi]\).

\( \lim _ { x + \infty } [ \sqrt { x ^ { 2 } + 2 x } - ( x + 1 ) ] \)

Determine el área encerrada entre las curvas \( y = x^2 \) y \( y = 4 - x^2 \), dado que se intersectan en más de dos puntos.

Calculate the volume of the solid formed by rotating the area between \( y = \sqrt{x} \) and \( y = 0 \) from \( x = 0 \) to \( x = 1 \) about the line \( y = -1 \) utilizing the washer method.