Carson M.

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$ y = x + 1 $ , $ y = 0 $ , $ x = 0 $ , $ x = 2 $ ; about the x-axis

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$ y = \frac{1}{x} $ , $ y = 0 $ , $ x = 1 $ , $ x = 4 $ ; about the x-axis

Differentiate the function.
$ z = \frac {A}{y^{10}} + Be^y $

If $ f(x) = 3x^2 - x^3 $, find $ f'(1) $ and use it to find an equation of the tangent line to the curve
$ y = 3x^2 - x^3 $ at the point $ (1, 2) $.

If $ g(x) = x^4 - 2 $, find $ g'(1) $ and use it to find an equation of the tangent line to the curve
$ y = x^4 - 2 $ at the point $ (1, -1) $.

Find $ f'(a) $.

$ f(x) = x^{-2} $