How Do Linear Approximations Differ from Tangent Lines in Calculus?

[sarahr]

what is the difference between a linear approximation and a tangent line?

my understanding is that the linear approximation is that it uses the tangent line at (a, f(a)) as an approximation to the curve y = f(x).

my question really is, then why in calculus I do they make an entirely separate section from equation of tangent lines for linear approximations? why call it something else?

 

[mathman]

Linear approximation is one application of the use of tangent line.