Question

Evaluate limx → 0(1+Tan(x))^Cot(x)

(a) 1

(b) e

(c) ln(2)

(d) e^2

This question was posed to me in an international level competition.

This intriguing question comes from Limits and Derivatives of Several Variables topic in section Partial Differentiation of Engineering Mathematics

Answer 1

The correct answer is (b) e

The explanation is: limx → 0(1+Tan(x))^Cot(x) = limtan(x) → 0 (1+Tan(x))^^1⁄Tan(x) = limt → 0 (1 + t)^^1⁄t = e.