- Find the linear approximation to a function at a point.
- Calculate the differential of a given function.
- Chapter 4.2 Linear Approximation and Differentials
- p. 364: 62, 63, 67-70 all, 72-74 all
Exit problems of the session
Find the linear approximation to near .
Use appropriate linear approximation to estimate .
- Find the differential for and evaluate it at and .
- 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
- Local linearity (9:37) Estimate .
- Linear approximation of a rational function (7:10) Find a linear expression that approximates around .
- Comparing and (4:07) Let .
- Find the change in , , when and .
- Find differential when and .