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)

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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)

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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

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