Question:
The value of
\[
\lim_{x\to 1}\left(\frac{x^3-1}{x-1}\right)
\]
is
The value of
\[
\lim_{x\to 1}\left(\frac{x^3-1}{x-1}\right)
\]
is
Show Hint
Use \(x^3-1=(x-1)(x^2+x+1)\) for limits involving \(x\to 1\).
Updated On: May 7, 2026
- \(0\)
- \(1\)
- \(3\)
- Limit does not exist
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Factorize: \[ x^3-1=(x-1)(x^2+x+1) \]
Step 2: \[ \frac{x^3-1}{x-1} = \frac{(x-1)(x^2+x+1)}{x-1} \]
Step 3: Cancel \((x-1)\): \[ =x^2+x+1 \]
Step 4: Put \(x=1\): \[ 1^2+1+1=3 \] \[ \boxed{3} \]
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