nerdychick
New member
- Joined
- Oct 13, 2013
- Messages
- 1
Fixed points and limits
- Thread starter nerdychick
- Start date
- Joined
- Feb 4, 2004
- Messages
- 16,550
For other readers, the text in the graphic appears to be as follows.
\(\displaystyle \mbox{Consider the difference equation}:\)
. . . . .\(\displaystyle x_{n+1}\, =\, 0.75x_n\, +\, 25\)
\(\displaystyle \mbox{(1) Find the fixed point(s) (steady state(s)) for the difference equation.}\)
\(\displaystyle \mbox{If there is only one fixed point, what is it? If there are multiple}\)
\(\displaystyle \mbox{fixed points, input the largest one}\)
Answer: 100
\(\displaystyle \mbox{(2) Take }\, x_0\, =\, 0\, \mbox{ and determine the limit of }\, x_n\, \mbox{ as }\, n\)
\(\displaystyle \mbox{goes to infinity.}\)
\(\displaystyle \mbox{Consider the difference equation}:\)
. . . . .\(\displaystyle x_{n+1}\, =\, 0.75x_n\, +\, 25\)
\(\displaystyle \mbox{(1) Find the fixed point(s) (steady state(s)) for the difference equation.}\)
\(\displaystyle \mbox{If there is only one fixed point, what is it? If there are multiple}\)
\(\displaystyle \mbox{fixed points, input the largest one}\)
Answer: 100
\(\displaystyle \mbox{(2) Take }\, x_0\, =\, 0\, \mbox{ and determine the limit of }\, x_n\, \mbox{ as }\, n\)
\(\displaystyle \mbox{goes to infinity.}\)