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Find a first degree approximation of f (x) = In x centered at x = 1.

Find a first degree approximation of f (x) = In x centered at x = 1.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Lab 4 (2).pdf 1 / 2 110% + Press F11| to exit full screen Z ASL 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
Transcribed Image Text:Lab 4 (2).pdf 1 / 2 110% + Press F11| to exit full screen Z ASL 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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