1.) Show that the functions f1(x)=5^x, f2(x)=5^(x-3), ans f3(x)=5^x + 3^x all grow at the same rate as x approaches infinity.
2.) Determine whether each integral converges or diverges.
a.) integral from 0 to 2 of (dx)/(4 - x^2)
b.) integral from 0 to infinity of (5 + cosx) e^(-x)dx
c.) integral from 0 to infinity of x^(-3)dx
3.) Evaluate the integral from 0 to 3 of (dx)/(the square root of (9 - x^2))dx or state that it diverges.
4.) Evaluate the integral from e to infinity of (3dx)/(x(lnx)^2) or state that it diverges.
5.) Find the area of the region in the first quadrant that lies under the graph of
y= (3x^2 + x) e^(-x)
6.) Use partial fractions to evaluate the integral of (2x + 4)/ (x^3 - 2x^2) dx
Sequences and improper integrals are investigated. The solution is detailed and well presented.