• Support PF! Buy your school textbooks, materials and every day products Here!

The limit as x approaches infinity

  • Thread starter Goldenwind
  • Start date
  • #1
146
0

Homework Statement


(3x-2) / (9x+7)

As x approaches infinity.

The Attempt at a Solution


I know the procedure, but am then stuck:
- Rearrange
- Plug in infinity for x
- Evaluate

Tried breaking it into 3x / (9x+7) - 2 / (9x+7)
The second thing would go to zero.
The first, no clue.

Maybe multiplying the original problem by something? Unsure what.

(Note: This is to help a friend. I myself am going to bed now, but they will be checking for replies. They're not allowed to use L'Hopital's rule, as it wasn't taught)
 
Last edited:

Answers and Replies

  • #2
378
2
factor out x from both num and den!
and plug in the infinity value without thinking
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,793
922

Homework Statement


(3x-2) / (9x+7)

As x approaches infinity.

The Attempt at a Solution


I know the procedure, but am then stuck:
- Rearrange
- Plug in infinity for x
- Evaluate
No, you don't "know the procedure". Only in the most trivial limits (limits of continuous functions where, by definition, the limit is the value of the function, can)you "plug" the target point into the formula. And certainly you can't "plug infinity" into this formula because it is only defined for real numbers and "infinity" is not a real number.

Tried breaking it into 3x / (9x+7) - 2 / (9x+7)
The second thing would go to zero.
The first, no clue.

Maybe multiplying the original problem by something? Unsure what.

(Note: This is to help a friend. I myself am going to bed now, but they will be checking for replies. They're not allowed to use L'Hopital's rule, as it wasn't taught)
It is true, however, that limit, as "x goes to infinity", of 1/x is 0 and 0 is easy to use. In order to change from "x" to "1/x" divide both numerator and denominator by x (that is the same as rootX's "factor x from numerator and denominator").
 
Last edited by a moderator:

Related Threads for: The limit as x approaches infinity

  • Last Post
Replies
7
Views
26K
  • Last Post
Replies
14
Views
3K
  • Last Post
Replies
2
Views
810
  • Last Post
Replies
8
Views
2K
Replies
7
Views
1K
  • Last Post
Replies
5
Views
850
Replies
15
Views
66K
Replies
1
Views
5K
Top