​What is the value of $$\lim _{x \rightarrow 12} \frac{x^3-1728}{x-12} ?$$​​

Correct option is D

​$$\begin{aligned}&\text{We are asked to evaluate the limit:} \\&\lim_{x \to 12} \frac{x^3 - 1728}{x - 12} \\[10pt]&\text{Note that } 1728 = 12^3, \text{ so the expression becomes:} \\&\frac{x^3 - 12^3}{x - 12} \\[10pt]&\text{Use the identity:} \quad a^3 - b^3 = (a - b)(a^2 + ab + b^2) \\[10pt]&\text{Applying it here:} \quad x^3 - 12^3 = (x - 12)(x^2 + 12x + 144) \\[10pt]&\text{So,} \\&\frac{x^3 - 12^3}{x - 12} = \frac{(x - 12)(x^2 + 12x + 144)}{x - 12} \\[10pt]&\text{Cancel the common factor } (x - 12), \text{ and you're left with:} \\&x^2 + 12x + 144 \\[10pt]&\text{Now take the limit as } x \to 12: \\&12^2 + 12 \cdot 12 + 144 = 144 + 144 + 144 = 432 \\[10pt]\end{aligned}$$​​