Use Graph To Investigate Limit

  • Thread starter nycmathguy
  • Start date
  • #1
Summary:: Use Graph To Investigate Limit

Use the graph to investigate the limit of f(x)
as x tends to 0.

Let me see.

I got to use the graph to investigate the limit of f(x) as x tends to 0 from the left and right.

Let y = f(x).

The given function can also be expressed as f(x) = | x |.

The limit of (-x) as x-->0 from the left is positive infinity.

The limit of (x) as x-->0 from the right is positive infinity.

The limit of f(x) as x-->0 from the left and right at the same time is positive infinity.

Can I say the limit of f(x) is positive infinity?
 

Attachments

  • th.jpeg-5.jpg
    th.jpeg-5.jpg
    5.8 KB · Views: 51
Last edited by a moderator:

Answers and Replies

  • #2
phinds
Science Advisor
Insights Author
Gold Member
2022 Award
18,148
10,978
The limit of (-x) as x-->0 from the left is positive infinity.

The limit of (x) as x-->0 from the right is positive infinity.

The limit of f(x) as x-->0 from the left and right at the same time is positive infinity.

Can I say the limit of f(x) is positive infinity?
Only if you think for some unfathomable reason that zero and positive infinity are the same thing.

You CLEARLY show a graph in which the y value goes to zero as the x value approaches zero. How can you think that this is positive infinity?
 
  • #3
36,708
8,701
You CLEARLY show a graph in which the y value goes to zero as the x value approaches zero. How can you think that this is positive infinity?
+1
 
  • #4
Only if you think for some unfathomable reason that zero and positive infinity are the same thing.

You CLEARLY show a graph in which the y value goes to zero as the x value approaches zero. How can you think that this is positive infinity?

I was thinking about the V shape formed by the graph of y = | x |. In quadrants 1 and 2, the graph starts at (0, 0) and shoots upward through quadrants 1 and 2 into eternity. However, thinking about it, as I walk toward zero on the x-axis from the left and right, the graph does reach a height of zero. The limit is 0.
 
  • #5
+1

What does +1 mean? Please, read my reply to phinds.
 
  • #6
36,708
8,701
What does +1 mean? Please, read my reply to phinds.
+1 means I agree with what phinds wrote.
I was thinking about the V shape formed by the graph of y = | x |. In quadrants 1 and 2, the graph starts at (0, 0) and shoots upward through quadrants 1 and 2 into eternity. However, thinking about it, as I walk toward zero on the x-axis from the left and right, the graph does reach a height of zero. The limit is 0.
Since the problem was to find the limit as x approaches zero, it's immaterial what the graph does for large x or for very negative x.
 
  • #7
+1 means I agree with what phinds wrote.
Since the problem was to find the limit as x approaches zero, it's immaterial what the graph does for large x or for very negative x.
What about if the graph is y = -| x | as x tends to 0? You said: "...it's immaterial what the graph does for large x or for very negative x." Can you provide an example using another function?

By the way, are you the same MarkFL from Florida? He is very popular in other math forums.
 
  • #8
phinds
Science Advisor
Insights Author
Gold Member
2022 Award
18,148
10,978
What about if the graph is y = -| x | as x tends to 0? You said: "...it's immaterial what the graph does for large x or for very negative x." Can you provide an example using another function?
Do you have some belief that -0 is different from +0 ?

By the way, are you the same MarkFL from Florida? He is very popular in other math forums.
click on his avatar to see that he is from Washington State
 
  • #9
36,708
8,701
What about if the graph is y = -| x | as x tends to 0?
Same limit value.
$$\lim_{x \to 0} |x| = \lim_{x \to 0} -|x| = \lim_{x \to 0} x^2 = \lim_{x \to 0} x^3 = 0$$
You said: "...it's immaterial what the graph does for large x or for very negative x." Can you provide an example using another function?
If you're investigating the limit of some function as x approaches zero, why would you want to check on what happens if x is very large or very negative? That's what I meant by "it's immaterial".
 
  • #10
Same limit value.
$$\lim_{x \to 0} |x| = \lim_{x \to 0} -|x| = \lim_{x \to 0} x^2 = \lim_{x \to 0} x^3 = 0$$
If you're investigating the limit of some function as x approaches zero, why would you want to check on what happens if x is very large or very negative? That's what I meant by "it's immaterial".

I get it now thanks to you. This is a great site.
 
  • #11
Do you have some belief that -0 is different from +0 ?

click on his avatar to see that he is from Washington State

No. Obviously, -0 = +0 = no value. Yes, you are right. He is not MarkFL. I do miss MarkFL. What an incredible mathematician he truly is. Member jonah ruined my friendship with MarkFL. Sorry but I needed to bring this into light.
 

Suggested for: Use Graph To Investigate Limit

  • Last Post
Replies
7
Views
463
  • Last Post
Replies
6
Views
413
Replies
6
Views
440
  • Last Post
Replies
3
Views
391
  • Last Post
Replies
15
Views
676
  • Last Post
Replies
2
Views
337
  • Last Post
Replies
30
Views
1K
  • Last Post
Replies
1
Views
387
Replies
11
Views
383
Replies
2
Views
375
Top