Question

For all x∈(0, 1) :

• A. e^x< 1 + x
• B. log_e(1 + x) < x
• C. sin x > x
• D. log_ex > x

Answer 1

Answer: (B)

log_e(1 + x) < x

Answer 2

x∈(0, 1), put x = 1/2

(1) e^x < 1 + x (2) log(1 + x) < x

$\sqrt{e}$< 3/2 log 3/2 < 1/2

false log3 – log2 < 0.5 true