Evaluate lim (x -> 0) [ (e^(2x) - 1) / x ].
Answer and explanation
Correct answer: A. 2
- Step 1: Direct substitution gives 0/0. Apply L'Hopital's Rule.
- Step 2: Differentiate numerator and denominator: lim (x -> 0) [ 2 e^(2x) / 1 ] = 2 e^0 = 2 * 1 = 2.
Answer
2.
Why not the others: '1' assumes the standard derivative without inner coefficient 2; '0' evaluates the numerator at 0 without dividing; 'e' confuses e^0 with e^1.
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