Optimization Extended
A steel pipe is being carried down a hallway 3m wide. At the end of the hall there is a
right-angled turn into a narrower hallway 2m wide. What is the longest length of pipe that
can be carried horizontally around this corner?
A pipe
PROBLEM 18 : Find the length of the shortest ladder that will reach over an
8-ft. high fence to a large wall which is 3 ft. behind the fence. (See diagram.)
SOLUTION
Let variable L be the length of the ladder resting on the top of the fence and
touching t
- 1 : preliminaries, Limits and continuity
Assignment
Note: Figures for the problems are on the last
1. Find all numbers
(i) lr-31 :B
(iii) lr-31 >8
r
(")1"-1l+lu_21
2'
page.
for which
<s
(ii)lr_31 <B
1r_rln lr_21>3
("ij lr_lllr_21 :'3
(tu;
(7,8126) which