A) It is given that the solution set of 1 / ( x + 1) < ax ^ 2 + bx + c, where a, b and c are real constants,

is (-infinity , -3) U (-2, -1) U (1 , infinity). By considering the graph of ax ^ 2 + bx + c, and forming a system of linear equations, determine the values of a, b and c.





b) The finite region in the first quadrant bounded by the curves x^ 2 + y ^ 2 = 9, y = e ^ (x ^ 2 /4), the x axis and the y-axis is denoted by R. Find the volume of the solid of revolution formed when R is rotated through 2 pie radians about the x-axis.

A) It is given that the solution set of 1 / ( x + 1) %26lt; ax ^ 2 + bx + c, where a, b and c are real constants,
Hint:


a) Let f(x) = 1/(x+1) - ax^2 + bx + c. Then you can find four critical points at which either f(x) = 0 or f(x) is undefined.





b)Solving the system of the two given equations gives the intersection point coordinate: x=1.85298 and y = 2.35934.





V = pi [int e^ (x ^ 2 /2 dx (0..1.85298) + int sqrt(9 - x^2) dx (1.85298..3)] = 22.709 unit^3
Reply:Take a look in that calc book, it will take you through a procedure to solve problems like this. Use the formula provided to find the volume of a rotation, I believe you will have to use integration. It is similar to finding the area under the curve, except the curve is rotated around an axis.
Reply:X=76-1