1. Give the volume of the solid generated by revolving the region bounded by the graph of y=ln (x), the x-axis, the lines x=1 and x=e, about the y-axis.
a) 0.25pi(e4 -1)
b) 0.5pi(e2 +1)
c) 0.5pi(e2 +1)
d) 0.25pi(e4 +1)
2. Find the slope of the tangent line to the graph of f at x = 4, given that f(x) = -x2 + 4sqrt(x).
a) -7
b) -10
c) -8
d) -9
3. Give the approximate average value of the function f(x) = 4x ln (2x) over the interval [1, 4].
a) 15.54
b) 16.71
c) 19.71
d) 12.54