The limit problem lim (x->0) \frac{x - sinx}{x^{3}} can be effectively solved using L'Hôpital's Rule, which applies when both the numerator and denominator approach zero. By differentiating the numerator and denominator, the limit simplifies to lim (x->0) \frac{1 - cosx}{3x^{2}}, which can be further evaluated. The key takeaway is that understanding the relationship sin(x)/x = 1 as x approaches 0 is crucial for simplifying the limit, but L'Hôpital's Rule provides a more straightforward approach for this specific problem.
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