Thread: 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?

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 .

Originally Posted by CountingPenguins

Any suggestions?

Some more details: now, for every choose .

[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

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.


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?

To prove , you need to show that for . So in this case, to prove , you need to show .




So by letting , the proof will follow.

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.