Scary Limit

Calculus Level 4

\[ \large\varphi = \displaystyle\lim_{x\rightarrow 0} \dfrac{\alpha - \sqrt{\alpha^2 - x^2} - \dfrac{x^2}{4}}{x^4}, \quad \alpha >0\]

If \(\varphi\) is finite, then find the value of \(\varphi + \alpha\) correct up to 4 decimal places.

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