# Turtles all the way

Calculus Level 4

Consider a function $f(x)$ that satisfies

• $f'(x) = \dfrac{1}{x + \dfrac{1}{x + \dfrac{1}{...}}}$, and
• $f(0) = 0$.

What is all of the possible values of $f(3)$ (to 2 decimal places)?

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