Question

help!!!

Answer 1

prove that for \[\left| t \right|\le 1/2\]

\[\left| Log(1+t)-t \right|\le 2t ^{2} \]

any idea?

Answer 2

Try taylor expansion for log(1+t)

Answer 3

\(|\ln (1+t) - t| = t - \ln(1+t)\) when \(|t| \le 1/2 \) :

the inequality to prove is same as proving :

\[\int \limits_0^t 1- \frac{1}{1+t} - 4t \le 0\]

Answer 4

thank you for your help..