Indirect limits

Calculus Level 3

\[ \large f(x) = \frac{(e^x-1)^4}{\sin \left(\frac{x^2}{\lambda^2} \right) \ln \left(1 + \frac{x^2}2 \right) } \]

For non-zero \(x\), denote the function \(f\) as above. If \(f(0)= 8\) and \(f\) is continuous then what is the possible value of \(\lambda\)?

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