4148. Washers vs. shells Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk>washer and shell methods. Check that your results agree and state which method is easier to apply. y = 6>1x + 32, y = 2 - x; revolved about the x-axis

Overview week of 9/12/16 3.3 Rules of Differentiation Power of X: d n (n1) Power Rule: / Xdx= nX Quotient Rule: / f(x)/g(x) = [(f(x) * g(x)) – (f(x) * g(x))] / [g(x)] 2 dx Product Rule: / [dxx) * g(x)] = [f(x) * g’(x)] + [g(x) * f’(x)] Chain Rule: / [dxg(x))] = [f(g(x))]’ * g’(x) Constant Multiple: Power rule d /dx(cf(x)) = c * f ’(x) 3.4 Product and Quotient Rules Product Rule: While [f(x) +/ g(x)]’ = f ‘(x) +/ g’(x), The same does not apply to multiplication And division. [f(x)g(x)] ≠ f ‘(x) * g’(x) Instead: [f(x)g(x)] = [f(x) * g’(x)] + [g(x) * f’(x)] Products of multiple functions: (fg)’ = f’g + fg’ (fgh)’ = f’gh + fg’h + fgh’ (fghi)’ = f’ghi + fg’hi + fgh’i + fghi’