Suppose that f e C(R) and that | If(x)|dx converges. Show then that 2 f(x)| sin nx|dx sx)dx. lim n00

What is the purpose of the Intermediate Value Theorem?

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?

Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?