# Limits As X Approaches Infinity and Negative Infinity

1. Sep 8, 2008

### dylmans

1. The problem statement, all variables and given/known data
Find the limit of each function
(a) as x approaches infinity and
(b) as x approaches negative infinity

2. Relevant equations
1. g(x)=1/(2+(1/x))

2. f(x)=(2x+3)/(5x+7)

3. h(x)=(9x^4+x)/(2x^4+5x^2-x+6)

3. The attempt at a solution
I don't know where to start.

2. Sep 8, 2008

### Dick

Put a large positive and a large negative number into each. Does that suggest what the answer might be? Now can you figure out how to prove it? This typically means dividing the numerator and denominator by the dominant power.

3. Sep 8, 2008

### dylmans

i dont exactly get what you mean. what number would i need to put in? answers for number 1 are both 1/2 and the answers for number 2 are both 2/5. the answer for 3 isn't in the book

4. Sep 8, 2008

### Dick

I was just suggesting you experiment numerically to get a feel for what a limit means. Try x=-100000 and x=100000. Are the answers close to what the book said? Now just start with the first one. What the limit of 1/x as x goes to either infinity?

5. Sep 8, 2008

### dylmans

1 over infinity?

6. Sep 8, 2008

### Dick

No, no. LIMIT 1/x as x goes to infinity. It APPROACHES an honest to God REAL number. What is that actual number? Infinity is not a number. 1/10, 1/100, 1/1000, 1/10000. What are they getting closer and closer to?

7. Sep 8, 2008

### dylmans

they're getting closer to infinity...

8. Sep 8, 2008

### Dick

No, son, they are getting closer to zero. Let's rewrite them in decimal 0.1, 0.01, 0.001, 0.0001, etc.

Last edited: Sep 8, 2008
9. Sep 8, 2008

### dylmans

oh duh, ok, so what do i need to do to figure out the answer, plug in zero?

10. Sep 8, 2008

### Dick

Well, what's 1/(2+almost zero)? For the second one divide numerator and denominator by x. Now you have (2+almost zero)/(5+almost zero).

11. Sep 9, 2008

### dylmans

ok, i think i get those two better. so for 3, id start by trying to factor, which i don't see anything that factors off the top of my head...

12. Sep 9, 2008

### Dick

Divide numerator and denominator by x^4. As x->infinity, x^4 is the large term. The rest go to zero for the same reason 1/x did.

13. Sep 9, 2008

### dylmans

ok, i think i get it now. so the answer for number 3 would be 9/2 as it approaches infinity and the same as it approaches negative infinity?

14. Sep 9, 2008

### dylmans

ok so the next problem is the limit as x approaches infinity for (2+x^1/2)/(2-x^1/2). the answer i got was -1.

15. Sep 9, 2008

### Dick

I believe that.

16. Sep 9, 2008

### dylmans

ok, that works, thanks for the help. i'll post if i run into anymore problems