Consider the functions f(x)= and g(x) = x, for x > 0. (a) Sketch the graphs...

 

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Consider the functions f(x)= and g(x) = x, for x > 0. (a) Sketch the graphs of y = f(x) and y = g(x) on the same axes, labelling the curves clearly. (b) Find the points of intersection of the curves, and hence show that the region bounded by the curves lies between 0 and 2 = 1. (c) Calculate the volume of the solid obtained by rotating the region bounded by y = f(x) = x and y = g(x) = x around the x-axis. Also sketch the solid and a typical "washer" (annulus) cross-section. (You can add this to your figure from (a).) Consider the functions f(x)= and g(x) = x, for x > 0. (a) Sketch the graphs of y = f(x) and y = g(x) on the same axes, labelling the curves clearly. (b) Find the points of intersection of the curves, and hence show that the region bounded by the curves lies between 0 and 2 = 1. (c) Calculate the volume of the solid obtained by rotating the region bounded by y = f(x) = x and y = g(x) = x around the x-axis. Also sketch the solid and a typical "washer" (annulus) cross-section. (You can add this to your figure from (a).)

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Lets solve each part step by step Part a To sketch the graphs of fx textrand and gx x2 on the same a... View the full answer