# Calculus

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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 in the link below. Please show your work.

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1. Find the area of R.
2. 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.
3. 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.

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