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Approximation by Differentials

A method for approximating the value of a function near a known value. The method uses the tangent line at the known value of the function to approximate the function's graph. In this method Δx and Δy represent the changes in x and y for the function, and dx and dy represent the changes in x and y for the tangent line.

Example: Approximate by differentials.
Solution:

is near , so we will use with x = 9 and Δx = 1. Note that .

Thus we see that This is very close to the correct value of

See also

Differential, infinitesimal

 


  this page updated 28-jul-14
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes