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In Problems 41–45, find a formula for the error E(x) in the tangent line approximation to the function near x = a. Using a table of values for E(x)∕(x − a) near x = a, find a value of k such that E(x)∕(x − a) ≈ k(x − a). Check that, approximately, k = f″(a)∕2 and that E(x) ≈ (f″(a)∕2)(x − a)2.
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Calculus: Single And Multivariable
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