COMEDK · Maths · 16. Limits
If \(\lim _{x \rightarrow 1} \dfrac{x^4-1}{x-1}=\lim _{x \rightarrow k} \dfrac{x^3-k^3}{x^2-k^2}\), then the value of K is
- A \(8\)
- B \(\dfrac{8}{3}\)
- C \(\dfrac{4}{3}\)
- D \(\dfrac{3}{4}\)
Answer & Solution
Correct Answer
(B) \(\dfrac{8}{3}\)
Step-by-step Solution
Detailed explanation
Evaluate the first limit: \(\lim _{x \rightarrow 1} \dfrac{x^4-1}{x-1} = \lim _{x \rightarrow 1} \dfrac{(x-1)(x^3+x^2+x+1)}{x-1} = \lim _{x \rightarrow 1} (x^3+x^2+x+1) = 1+1+1+1 = 4\). Evaluate the second limit:…
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