appl. of derivatives

is it correct ln(1+x)<x for -1<x<0????????????

1 Answers

see

let q(x) = ln(1+x) - x

diff q(x) and see that q(x) is inc in (-1,0)

also q(0) = 0

=> as fn is inc and interval is (-1,0)

q(x) < q(0)

therefore ln(1+x) - x <0

hence proved

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