Question

Let f(x) be a function such that f(1)=1 and for x≥1 f'(1)=i/(x2+f2(x)). Prove that the limit f(x) exists and the limit is less than 1+(π/4)

Answer 1

Just want to clear up a few things. First, is that supposed to say (since you can't have an i in the derivative) \[f'(1)=\frac{1}{x^2+f(x)^2}\] Second, does what limit exist? The limit as x approaches infinity?

Answer 2

yes... my bad

Answer 3

Use e-d definition to prove limit exists? Then show what the limit actually tends to show less than 1+pi/4?