3 the functions f and g are given by f x x and g x

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Unformatted text preview: of problems— 4 No calculator is allowed for these problems. 3. The functions f and g are given by f ( x ) = x and g( x ) = 6 - x. Let R be the region bounded by the x-axis and the graphs of f and g, as shown in the figure above. (a) Find the area of R. (b) The region R is the base of a solid. For each y, where 0 £ y £ 2, the cross section of the solid taken perpendicular to the y-axis is a rectangle whose base lies in R and whose height is 2y. Write, but do not evaluate, an integral expression that gives the volume of the solid. (c) There is a point P on the graph of f at which the line tangent to the graph of f is perpendicular to the graph of g. Find the coordinates of point P. 4. Consider a differentiable function f having domain all positive real numbers, a...
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