(e) Suppose that we wish to use a Taylor polynomial T₁ (x) for f(x) = x - ln (x) with center a = 1 such that our error |R₁ (x)] is less than 0.000001 = 10-6. Find the least integer value of n for which this is guaranteed to be true by Taylor's Inequality, and show how you used Taylor's Inequality. As part of you work, you should find a formula for the (n+1) derivative fn+1(x).

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