42 sketch the graphs of y sec x and y tan x for 0 x

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Unformatted text preview: at if the region below the graph of f (x) = 1/x, x ≥ 1, is revolved about the x-axis, then the surface area of the resulting solid is infinite (see Example 3). 42. Sketch the graphs of y = sec x and y = tan x for 0 ≤ x < π/2. Calculate the area of the region between the two curves. 43. Let be the region bounded by the coordinate axes, the √ graph of y = 1/ x, and the line x = 1. (a) Sketch . (b) Show that has finite area and find it. (c) Show that if is revolved about the x-axis, the solid obtained does not have finite volume. 44. Let be the region between the graph of y = 1/(1 + x2 ) and the x-axis, x ≥ 0. (a) Sketch . (b) Find the area of . (c) Find the volume of the solid obtained by revolving about the x-axis. (d) Find the volume of the solid obtained by revolving about the y-axis. 45. Let be the region bounded by the curve y = e−x an...
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