Tough Improper Integral Question

[ChicagoWhiteSox]

I have a tough improper integral question...

Question: If f is continuous on from zero to infinite and limit of f(x) as x approaches infinite is one. Is it possible for the integral f(x) from (0-lower limit) to (infinite-upper limit) to be convergent?



Consult textbook:

Calculus Early Transcendental 6th Edition by James Stewart (Chapter 7 Section 7.8 Exercise 79)

 

[BigGlenntheHeavy]

Unless one can show a counter example, I would say no.