3.9 Linear Approximation and Differentials

Linear Approximation or Tangent Line Approximation of f at a

Linearization of f at a

This gives a good approximation only "near" a

#2 Find the linearization L(x) at a=0 for

Then also examine the graph of f(x) and L(x), and a table comparing values, near 0

Find the linear approximation of the function

Illustrate by graphing g and the tangent line.

Differentials

Differential dy, dy = f '(x)dx

Delta y is the ACTUAL change in y

Find the differential of

#14 a) Find the differential of

#16 a) Find the differential dy if

b) Evaluate dy for x = 1 and dx = -0.01

#20 Compute and compare for , x =1, .

#28 Use linear approximation or differentials to estimate the given number:

Assignment: 3.9; pg. 193; 1, 3, 11-25 odd