(b) Find the elasticity of demand and supply at the equilibrium price for the demand function \( p=\sqrt{36-x^{2}} \) and supply function \( x=p^{2}-6 \), where \( p \) and \( x \) are price and quantity respectively.

Determine el volumen resultante de rotar la función \( f(x) = \frac{1}{x} \), desde \( x = 1 \) hasta \( x = 2 \), alrededor del eje y usando el método de lavadoras.

16) \( \int \frac{x^{5}+1}{x-1} d x \)

Cos \( \mathrm{x}=1-\frac{x^{2}}{2!}+\frac{x^{4}}{4!}-\frac{x^{6}}{6!}+\ldots \ldots \) Show that \( \mathrm{y}=\frac{\ln x}{x} \) has maximum value at \( \mathrm{x}=\mathrm{e} \)

OR Prove that \( y \frac{d y}{d x}+x=0 \) if \( x=\frac{1-t^{2}}{1+t^{2}} \quad y=\frac{2 t}{1+t^{2}} \) Determine whether the given function ?

Evaluate \( \lim _{x \rightarrow 0^{-}} \frac{5 x-4|x|}{3 x} \)