Learning Outcomes

1. Find the linear approximation to a function at a point.
2. Calculate the differential of a given function.

Textbook

• Chapter 4.2  Linear Approximation and Differentials

Textbook Assignment

• p. 364:    62, 63, 67-70 all, 72-74 all

WeBWork Assignment

• Application-Linearization
• Application-Differentials

Exit problems of the session

1. Find the linear approximation to near .

2. Use appropriate linear approximation to estimate .

3. Find the differential for and evaluate it at and .

Key Concepts

• A differentiable function can be approximated at by the linear function: • The differential is an independent variable that can be assigned any nonzero real number; the differential is define to be • For a function , if changes from to , then is an approximation for the change in . The actual change in is .

#### Videos and Practice Problems of Selected Topics

1. Local linearity (9:37) Estimate .
2. Linear approximation of a rational function (7:10) Find a linear expression that approximates around .
3. Comparing and (4:07) Let .
• Find the change in , , when and .
• Find differential when and .