Question 1 .
A 5 m ladder is leaning against a house when its base starts to slide away. By the time the base is 4 m from the house, the base is moving at a rate of 2 m/s.
(a) How fast is the top of the ladder sliding down the wall?
(b) At what rate is the area of the triangle formed by the ladder, wall, and the ground changing?
(c) At what rate is the angle ! between the ladder and the ground changing?
ladder wall of house!
Question 2.
You have been asked to design a 1000 cm3 can shaped like a right circular cylinder. What dimensions will use the least material?
Question 3.
The diameter of a tree was 25 cm. During the following year the circumference increased by 5 cm. Using calculus, find
(a) How much the tree's diameter has changed?
(b) What is the corresponding change in the tree's cross-section area?