Reference no: EM131073704

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