CALCULUS Understanding Its Concepts and Methods

Linear approximation

The
approximation *f*(*x*) ≈
*f*(*a*) + *f'*(*a*)(*x*
- *a*) is
called the linear approximation or
tangent line approximation to
*f*
at
*a*.

The function
*L*(*x*) =
*f*(*a*) + *f'*(*a*)(*x*
- *a*) is
called the linearization of
*f*
at
*a*.

The line
*y* = *L*(*x*)
is the best approximation to the function
*f*
by a line near the point
*x* = *a*,
*y* = *f*(*a*).

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.