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## Homework Statement

If f(x) = x ln (1+x), find an approximation for the increase in f(x) when x increases by δx.

Hence estimate the value of ln (2.1), given that ln 2 = 0.6931.

## Homework Equations

δy ≈ (dy/dx)δx

## The Attempt at a Solution

δy ≈ [ln (1+x) + x/(1+x)] δx

When x = 1,

x ln(1+x) = ln 2 ≈ 0.6931

I would like to find a value for x such that

x ln(1+x) = 2.1

However, I am unable to solve this equation. Also when I try to derive the value of δx from the answer given in my textbook , 0.72, I get 0.040931534, which is not a solution to

x ln(1+x) = 2.1

So I'm a bit stuck, and would appreciate any help someone might be able to offer.