Let f(x) be a function defined for x>=1, f(1)=1 and df/dx=1/(x^2+f(x)^2)
Prove that limf(x) exists and is less than 1+(pi/4)
Let be a function defined for , and
Prove that exists and is less than
Proof. Since , we know that f(x) is an increasing function. So, when , . Now ...
This shows how to prove that a limit exists and is less than a given value.