Linear Approximation

is the linear approximation or tangent line approximation for x near a

is the linear approx or tangent plane approx for (x, y) close to (a, b)

Definition: The Linearization of f(x, y) at (a, b) is defined as

Thus, the linear approximation of f at (a, b) can be written as for (x, y) close to (a, b)

Linear approximation can also be expressed as

or

for near the point