Limits
Standard Algebraic Limits
JEE Main
Grade 11
Question:
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 $k$ equals:
(1) $\frac{8}{3}$
(2) $\frac{4}{3}$
(3) $\frac{2}{3}$
(4) $\frac{3}{4}$
Step-by-Step Solution
Key Concept: $LHS = 4$. $RHS = \frac{3k^2}{2k} = \frac{3k}{2}$. Setting $\frac{3k}{2} = 4$ gives $k = \frac{8}{3}$.
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Correct Answer: (1)