Limits As X Approaches Infinity and Negative Infinity

Click For Summary

Homework Help Overview

The discussion revolves around finding the limits of various functions as x approaches infinity and negative infinity. The functions include rational expressions and polynomial terms, which are common in calculus.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss substituting large positive and negative values into the functions to gain insight into the limits. There is a focus on understanding the behavior of terms as x approaches infinity, particularly the significance of dominant powers in rational functions.

Discussion Status

Some participants have begun to clarify their understanding of limits, particularly regarding the behavior of 1/x as x approaches infinity. There is an ongoing exploration of how to apply these concepts to the given functions, with some participants expressing confusion about specific steps and terms.

Contextual Notes

Participants are working under the constraints of homework assignments, which may limit the information they can use or the methods they can apply. There is also a mention of discrepancies between their findings and textbook answers, prompting further investigation.

dylmans
Messages
13
Reaction score
0

Homework Statement


Find the limit of each function
(a) as x approaches infinity and
(b) as x approaches negative infinity


Homework 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)


The Attempt at a Solution


I don't know where to start.
 
Physics news on Phys.org
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.
 
i don't 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
 
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?
 
1 over infinity?
 
dylmans said:
1 over infinity?

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?
 
they're getting closer to infinity...
 
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:
oh duh, ok, so what do i need to do to figure out the answer, plug in zero?
 
  • #10
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
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
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
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
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
I believe that.
 
  • #16
ok, that works, thanks for the help. i'll post if i run into anymore problems
 

Similar threads

Limit Definition of Derivative as n Approaches Infinity
  • · Replies 20 ·
Replies
20
Views
3K
##\lim_{x \to0} \left(\dfrac{1}{\sin^2 x}-\dfrac{1}{x^2}\right)##
  • · Replies 5 ·
Replies
5
Views
2K
What is the difference in this limit?
  • · Replies 10 ·
Replies
10
Views
2K
Can the limit of a quotient of trig functions approach a specific value?
  • · Replies 2 ·
Replies
2
Views
2K
Find the derivative of the given function
  • · Replies 4 ·
Replies
4
Views
2K
Limit of Taylor Polynomial for Tn(x) as n Approaches Infinity
  • · Replies 2 ·
Replies
2
Views
1K
Find the coordinates of intersection between tangents and given curve
  • · Replies 15 ·
Replies
15
Views
3K
Limit of a_n as n Approaches Infinity & Zero
  • · Replies 24 ·
Replies
24
Views
2K
Help Taking the Limit as K goes to infinity
  • · Replies 14 ·
Replies
14
Views
3K
Limit as x approaches infinity.
  • · Replies 2 ·
Replies
2
Views
2K