# Taylor Polynom/Lagrange form om the remainder term.

2. For f(x) = (lnx)/x , x > 0, compute the Taylor polynomial P(x) of degree

three centered at the point x = e. Using the Lagrange form of the remainder term,

find an interval (e−δ, e+δ) in which the approximation of f by this polynomial is no worse than ε = 10^−2 ,

|f(x) − P(x)| < ε, x ∈ (e − δ, e + δ).

You may without proof use that 2 < e < 3.

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