Finding limits w/definition not shortcuts

My question is how to get the limit of lim ((3n+1)/(n+2))=3.

I used the trick where you divide every term by the variable with the largest exponent which is n in this case and came up with 3/1=3 which gives the lim = 0. I also checked it on it's graph.

However, I have to use "for each epsilon greater than 0 there exists a real number N such that for all n elements of the natural numbers n > N implies that absolute value of the sequence-s < epsilon.

Any suggestions? (Nerd)

Re: Finding limits w/definition not shortcuts

Quote:

Originally Posted by

**CountingPenguins** My question is how to get the limit of lim ((3n+1)/(n+2))=3.

I used the trick where you divide every term by the variable with the largest exponent which is n in this case and came up with 3/1=3 which gives the lim = 0. I also checked it on it's graph.

I'm sort of confused by your post. So are you suppose to prove that ?

If yes, then start with the inequality .

Re: Finding limits w/definition not shortcuts

Quote:

Originally Posted by

**CountingPenguins** Any suggestions? (Nerd)

Some more details: now, for every choose .

Re: Finding limits w/definition not shortcuts

[QUOTE=FernandoRevilla;662680]Some more details:

Thank you for your response, but can you tell me how you got from it isn't obvious to me. Those are the details I am missing.

Thanks,

CP

Re: Finding limits w/definition not shortcuts

Re: Finding limits w/definition not shortcuts

Re: Finding limits w/definition not shortcuts

Thank you very much for filling in all the blanks for me. I don't want the answer so much as how and why it works and you showed me how. Thanks.