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A.P. CALCULUS AB/BC

Chapter 7 - AP Questions - Worksheet # 1

Name ______________________________________________ Period ___________ 2003 AB-1/BC-1 Form B (Graphing Calculator)

Let f be the function given by f ( x) = 4x2 - x3, and let l be the line y = 18 - 3x, where l is tangent to the graph of f. Let R be the region bounded by the graph of f and the x-axis, and let S be the region bounded by the graph of f, the line l, and the x-axis, as shown above. a) Show that l is tangent to the graph of y = f ( x ) at the point x = 3. b) Find the area of S. c) Find the volume of the solid generated when R is revolved about the x-axis. 1995 AB-4/BC-2 (Graphing Calculator) The shaded regions R1 and R 2 shown at left are enclosed by the graphs of f (x) = x and g ( x ) = 2

2 x

.

a) Find the x- and y-coordinates of the three points of intersection of the graphs of f and g . b) Without using absolute value, set up an expression involving one or more integrals that gives the total area enclosed by the graphs of f and g . Do not evaluate. c) Without using absolute value, set up an expression involving one or more integrals that gives the volume of the solid generated by revolving the region R, about the line y = 5 . Do not evaluate.

1996 AB-2 (Graphing Calculator) Let R be the region in the first quadrant under the graph of y a) b) c) Find the area of R. If the line x = k divides the region R into two regions of equal area, what is the value of k. Find the volume of the solid whose base is the region R and whose cross sections cut by planes perpendicular to the x-axis are squares.

1 for 4 < x < 9. x

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