MHB Left hand and right hand limit at infinity

[Joel Jacon]

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]

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?

 

[Joel Jacon]

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.

 

[Jameson]

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.

 

[Joel Jacon]

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.

 

[Jameson]

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

That is correct! :)