Indirect limits

Calculus Level 3

f(x)=(ex1)4sin(x2λ2)ln(1+x22) \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 xx, denote the function ff as above. If f(0)=8f(0)= 8 and ff is continuous then what is the possible value of λ\lambda?

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