Problem 1.15. Can you paint this funnel? We consider the solid of revolution that is described by f(x)=x1 with x1. a) Sketch the function f(x). It describes a funnel of infinite length, or a "horn". b) Show that the funnel has the volume . c) Determine the surface S(L) of the piece of the funnel with x{1,L}. How does the function S(L) look like in the limit L ? What does this imply for the surface area of the funnel? d) Since the surface area of the funnel is infinite, one would expect that it can not painted with a finite amount of paint. On the other hand, its volume is finite such that it can be filled with a finite amount of paint. Wouldn't that imply that the surface is painted? How can that be? Problem 1.15. Can you paint this funnel? We consider the solid of revolution that is described by f(x)=x1 with x1. a) Sketch the function f(x). It describes a funnel of infinite length, or a "horn". b) Show that the funnel has the volume . c) Determine the surface S(L) of the piece of the funnel with x{1,L}. How does the function S(L) look like in the limit L ? What does this imply for the surface area of the funnel? d) Since the surface area of the funnel is infinite, one would expect that it can not painted with a finite amount of paint. On the other hand, its volume is finite such that it can be filled with a finite amount of paint. Wouldn't that imply that the surface is painted? How can that be