Probably L'Hospital

Calculus Level 4

Consider,
\(\displaystyle \psi (a) = \sqrt{a + \sqrt{ a + \sqrt{ a + \dots }}} \).

Evaluate: \(\displaystyle \lim_{ x \to 0 } \frac{ 1 - \psi ( 1-\cos x ) }{ 1 - \psi (x^2) }\)

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