Find a first degree approximation of f (x) = In x centered at x = 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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II. Second Degree Approximations centered at x = a.
Recall that the first degree approximation of a function f(x) centered at a (otherwise known as the
tangent line) is
L(x) 3D A + B(x — а)
where A = f(a) and B = f'(a). Similarly, if we want to approximate a function f(x) by a second
degree function P(x) centered at a, it is best to write P in the form
Р(х) 3D А + B(х — а) + C(х — а)2
6) Find a first degree approximation of f (x) = In x centered at x = 1.
7) Find a second degree approximation of f (x) = In x at x = 1.
%3D
8) Use graph paper to provide a detailed and accurate graph of f(x), L(x), and P(x) on the same
аxes.
9) Find a first degree approximation of f (x) = vx at x = 4.
10) Find a second degree approximation of f (x) = Vx at x = 4.
11) Use graph paper to provide a detailed and accurate graph of f(x), L(x), and P(x) on the same
аxes.
12) Prove that for a second degree polynomial centered at a to satisfy conditions (i), (ii), and (iii) we
II
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