+21 Daniel and Daniel walked into a math team meeting early and saw the following table on the board:
| x | 0 | 1 | 3 | 7 | 9 | 10 |
| f(x) |
a) The board states that the Taylor series of the equation f(x) = (20 π sinx) / x to the 5th order around x = 2 corresponds to the table, so Daniel fills in the table with the correct values. What is the competed table? Leave answer exact.
b) The other Daniel wants to find the point that represents the second smallest local minimum on the equation y = sin(x)e^(-|x|). He finds this point (the smallest local minimum of the function that is not equal to the global minimum) and calls its position (a, b). Darren walks in and wants to find the volume of the solid formed when the function is revolved around the horizontal line y = b, with the left and right x-bounds being x = 0 and x = a respectively. What is the volume of the solid? Represent answer as an integral.
