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If $\lim_{x \to 1} \frac{x^4 - 1}{x - 1} = \lim_{x \to k} \frac{x^3 - k^3}{x^2 - k^2}$, then $k$ is:
(1) $\frac{8}{3}$
(2) $\frac{3}{8}$
(3) $\frac{3}{2}$
(4) $\frac{4}{3}$
LHS: $\lim_{x\to 1} \frac{x^4-1}{x-1} = 4$. RHS: $\lim_{x\to k}\frac{3x^2}{2x} = \frac{3k}{2}$ (L’Hospital). So $\frac{3k}{2} = 4 \Rightarrow k = \frac{8}{3}$.
BETA
