The value oflimx→0 enx−1+nx+n22x2x3(n>0) is

The value of $lim_{x \to 0} \frac{e^{n x} - (1 + n x + \frac{n^{2}}{2} x^{2})}{x^{3}} (n > 0)$ is

Using series expansion of $e^{n x}$ the required
limit is equal to

$lim_{x \to 0} \frac{\frac{n^{3}}{6} x^{3} + \frac{n^{4}}{24} x^{4} + \dots}{x^{3}} = \frac{n^{3}}{6}$

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