Local Linear Approximation

Given a differentiable function then

whenever .

Approximate using local linear approximation:

1.

2.

Integration by parts

Evaluate the following indefinite integrals:

1. 
2. 
3. 

Sliding Ladders

A ladder 20 feet long leans against a house. Find the rate at which the top ladder is moving downward if the foot of the ladder is 12 feet away from the house and sliding along the ground away from the house at the rate of 2 feet per second. (Assume that the walls of the house are vertical.)