Answer: 4/e.
- A e/4
- B 4/e
- C 2/e
- D e/2
Correct answer: B. 4/e
Explanation: Taking logs converts this to ∫₀¹ ln(1+x) dx = 2ln2 − 1, so the limit is e2ln2 − 1 = 4/e.
As point Q slides along the curve toward P, the secant line PQ rotates into the tangent line at P, whose slope is the derivative.
Concept context
Rate of change, differentiation rules, and applications