\( \lim _{x \rightarrow \infty} \frac{(3-x)^{2}}{(x+4)^{3}-x^{3}} \)
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Using the binomial expansion, we have: \[ (x+4)^3 = x^3 + 3 \cdot x^2 \cdot 4 + 3 \cdot x \cdot 4^2 + 4^3 = x^3 + 12x^2 + 48x + 64 \] Subtract \(x^3\) from this: \[ (x+4)^3 - x^3 = 12x^2 + 48x + 64 \] Show more…
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