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Let $f : \mathbb{R} \to \mathbb{R}$ be defined as
$$f(x) = \begin{cases} x^5 \sin\left(\dfrac{1}{x}\right) + 5x^2, & x < 0 \ 0, & x = 0 \ x^5 \cos\left(\dfrac{1}{x}\right) + \lambda x^2, & x > 0 \end{cases}$$
The value of $\lambda$ for which $f’’(0)$ exists, is ______.
BETA
