The discussion revolves around the limits of the function $\frac{1}{x}$ as $x$ approaches 0 from both the left and the right. Participants explore the concepts of left-hand limit (LHL) and right-hand limit (RHL), seeking to understand why the limit does not exist at this point.
Participants generally agree on the outcomes of the left-hand limit being negative infinity and the right-hand limit being positive infinity. However, there is initial confusion regarding the behavior of the limits, which is clarified through discussion.
Some assumptions about the behavior of the function near zero are explored, but there are no explicit resolutions to the initial confusion regarding the limits.
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?
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?
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.
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.
pcforgeek said:I finally understand now. LHL is negative infinity and RHL is positive infinity.