The problem is:

Verify the given linear approximation at a=0. Then determine the values of x for which the linear approximation in accurate to within 0.1.
LN(1+x) ≈ x

I found f(0) = 0 and f'(0) = 1
I have an equation:
LN (1+x) -(.1) < x < LN(1+x) + 1

The answer is -.383 < x < .516
How did they get those numbers? I know that the line I found approximates the graph of LN(x+1), but I don't know how to determine accuracy to .1

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