19/05/14 01:47:28.49 spD4KjCm.net
log(x) は単調増加だから、x≧1/e でも x≦1/e でも
∫[1/e, x] {log(u) - log(1/e)｝du ≧ 0,
∴ x･log(x）= -1/e + ∫[1/e, x] {log(u) - log(1/e)｝du ≧ -1/e,
∴ x^x ≧ exp(-1/e) = 0.6922････
19/05/14 01:47:28.49 spD4KjCm.net
log(x) は単調増加だから、x≧1/e でも x≦1/e でも
∫[1/e, x] {log(u) - log(1/e)｝du ≧ 0,
∴ x･log(x）= -1/e + ∫[1/e, x] {log(u) - log(1/e)｝du ≧ -1/e,
∴ x^x ≧ exp(-1/e) = 0.6922････