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How to find specified limits

Hey guys,

I know these examples are simple but i tried to solve them for about an hour and haven't succeed. Can someone help me?

Thank you in advance!

Original post by Stellie

Hey guys,

I know these examples are simple but i tried to solve them for about an hour and haven't succeed. Can someone help me?

Thank you in advance!

Here is an example of how to do the first one:

After expanding it becomes:

lim (2n^3 _n - 3)/(8n^3 - 12n^2 + 6n - 1)

Now divide top and bottom by n^3 to give:

lim (2+ 1/n^2 - 3/n^3)/(8 - 12/n + 6/n^2 - 1/n^3)

All 1/n or 1/n^2 etc. terms go to 0 as n approaches infinity, so we are then left with:

lim (2/8) = 1/4

Reply 2

Dingooose

Einstein has given the answer that I was going to give, so I guess all I'll do is write it in nice LaTex for you. If you're still working on it then don't look at the answer (I'll include it in a spoiler).

Spoiler

I don't know if this is the best way of doing it but it works. You can work out the other problems using the same method.