|
|
|
|
||
|
|
||
|
|
Authors: Bill Davis, Horacio Porta, and Jerry Uhl ©1999 Producer: Bruce Carpenter Publisher: Math Everywhere, Inc. Distributor: Wolfram Research, Inc. |
| EXAMPLE
SOLUTION |
G.2) Line fundamentals*
G.2.b)
Put
What do you say are the limiting values
and
First, I'll enter this function in
Positive Infinity
I'll check out some values of f for large x's:
I'm guessing the limit is 2. If this is correct then a graph of f should flatten out at a height of 2 as x gets bigger. Let's check.
Plot[f[x],{x,0,100000}]
2 it is then.
Negative Infinity
Let's go right to a graph.
Plot[f[x],{x,-100000,0}]
Looks like 2 again.
The formula
It seems that both limits are 2. Does that make sense according to the formula? Let's take a look at the formula again...
When x is really really really big, the x6 term dominates. That means f[x] will look a lot like 
, which is the same as 2. So, 2, does seem like a good limit of f for positive or negative infinity.
| Send questions or comments to website@socrates.math.ohio-state.edu | Copyright © 1998-2009, Calculus&Mathematica |