MHB Left hand and right hand limit at infinity

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The discussion centers on evaluating the limit of the function 1/x as x approaches 0 from both the left and right. The left-hand limit (LHL) as x approaches 0 from the negative side results in negative infinity, while the right-hand limit (RHL) as x approaches 0 from the positive side leads to positive infinity. Since the LHL and RHL do not converge to the same value, the overall limit does not exist. The conversation emphasizes the importance of understanding these limits to grasp the behavior of the function near the point of discontinuity. Thus, the limit of 1/x as x approaches 0 is confirmed to be non-existent.
Joel Jacon
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Show that $\lim_{{x}\to{0}}$ $\frac{1}{x}$ does not exist?
Please tell me how to make LHL and RHL for this? Explain me all steps used?
 
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pcforgeek said:
Show that $\lim_{{x}\to{0}}$ $\frac{1}{x}$ does not exist?
Please tell me how to make LHL and RHL for this? Explain me all steps used?

Hi pcforgeek, (Wave)

Welcome to MHB!

We don't really give out answers or do problems fully for others, rather help you solve it yourself. So let's do that. :)

Ok, starting from the left: $$\lim_{{x}\to{0^-}}\frac{1}{x}$$

What do you get when you type in $$\frac{1}{-.5}$$ on your calculator? What about $$\frac{1}{-.1}$$? $$\frac{1}{-.01}$$? Notice that these numbers are walking closer and close to 0 from the negative side of it. Any idea where this trend is going?
 
Jameson said:
Hi pcforgeek, (Wave)

Welcome to MHB!

We don't really give out answers or do problems fully for others, rather help you solve it yourself. So let's do that. :)

Ok, starting from the left: $$\lim_{{x}\to{0^-}}\frac{1}{x}$$

What do you get when you type in $$\frac{1}{-.5}$$ on your calculator? What about $$\frac{1}{-.1}$$? $$\frac{1}{-.01}$$? Notice that these numbers are walking closer and close to 0 from the negative side of it. Any idea where this trend is going?

I already know that as the denominator becomes smaller and smaller and closer to zero the value becomes infinity. Can you tell me how to get right hand limit and left hand limit for this problem.
 
pcforgeek said:
I already know that as the denominator becomes smaller and smaller and closer to zero the value becomes infinity. Can you tell me how to get right hand limit and left hand limit for this problem.

I was showing you how to calculate the left hand limit actually, which does not approach infinity. Did you try what I asked? Try again and tell me what the trend is for values approaching 0 from the left. Plug in those values I suggested and you should see a pattern.
 
Jameson said:
I was showing you how to calculate the left hand limit actually, which does not approach infinity. Did you try what I asked? Try again and tell me what the trend is for values approaching 0 from the left. Plug in those values I suggested and you should see a pattern.

I finally understand now. LHL is negative infinity and RHL is positive infinity.
 
pcforgeek said:
I finally understand now. LHL is negative infinity and RHL is positive infinity.

That is correct! :)
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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