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