Question

limit as x approaches 3 of (1+(1/3)x) =2

Answer 1

Do you have a question about the limit?

Answer 2

delta and epsilon

Answer 3

i basically need to show proof

Answer 4

What do you have so far?

Answer 5

\[\lim_{x \rightarrow 3}1+\frac{ 1 }{ 3 }x=2\]Is this the limit you're talking about?

Answer 6

3-3e<x<3e+3

Answer 7

yess

Answer 8

You went in the wrong direction
You started with abs(1+x/3-2)<e = abs(x/3-1)<e
Mutliply through by 3 you have abs(x-3)<3e. See how this is related to your delta

Answer 9

We prove the limit through substitution. Substitute 3 in for x in the limit.\[\lim_{x \rightarrow 3}1+\frac{ 1 }{ 3 }x=1+\frac{ 1 }{ 3 }(3)=1+1=2\]Therefore, as x approaches 3, the limit approaches 2.

Answer 10

@ehhhlalaxd

Answer 11

how would you prove it showin epsilon and delta

Answer 12

ahhh i see @Xavier

Answer 13

Oh you are talking about delta epsilon proofs of limits, no wonder you were using absolute value and stuff. I would show but I'm too tired at the moment and going to sleep. You can search up delta-epsilon proofs of limits on google, there is some easy to follow guides. Ciao.

Answer 14

thank you too genius!