Let $f(x) = \mathop {\text{Lim}}\limits_{h \to 0} \frac{1}{h} \int\limits_x^{x + h} \frac{dt}{t + \sqrt{1 + t^2}}$,then $\mathop {\text{Lim}}\limits_{x \to -\infty} x \cdot f(x)$ is
- Aequal to $0$
- Bequal to $\frac{1}{2}$
- Cequal to $1$
- Dnon-existent
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