Linear Approximations

Definition (Linear Approximation) The approximation



is called the linear approximation of at and the function



is called the linearization of at

    The equation of the tangent line to the curve at is



which is so that in fact we have Thus when using differentials to approximate, that is, when using   to approximate we are using the tangent line at as an approximation to the curve when is near

Example (Linear Approximation) Find the linearization for the following functions at the given value.

(a) Find the linearization of   at

    Solution. The linearization of the function at is







Therefore, we have the linear approximation for when is near 0.

(b) Find the linearization of   at

    Solution. The linearization of the function at is







Therefore, we have the linear approximation for when is near 0.

• print this page
• pages linking here
• related pages

Cite this as:
Linear Approximation
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/linear-approximation.html