(f) \( \lim _{x \mapsto 0^{-}} \frac{-2 \cdot x^{2}}{x^{4}+x^{3}} \)

Answer any THREE. \( \lim _{x \rightarrow 1}\left(\frac{1}{x-1}-\frac{1}{\ln x}\right) \)

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

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

d) \( \lim _{x \rightarrow 1} \frac{\ln x}{x^{2}-1}= \)

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.