In single-variable calculus, linear approximation is the idea that at a point, as we zoom in to the function, we can approximate the value of the function with a tangent line. For sufficiently close to , we can use .
In multivariable calculus, we instead discuss the idea of a plane: the tangent plane, where we can approximate a curved surface by a plane that is tangent to the surface at the given point.
In both cases, the equation is the first-order Taylor series, and functions must be differentiable at that point.
