Use the epsilon definition of the limit that if for every positive real number , there exists a real number such that whenever , to prove

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- February 3rd 2010, 01:14 PMvuze88Limits
Use the epsilon definition of the limit that if for every positive real number , there exists a real number such that whenever , to prove

- February 3rd 2010, 07:46 PMCalculus26
I'm assuming your function is (x+3)/(x^2-9)

See attachment - February 4th 2010, 12:04 AMvuze88
thanks for the help. So is it not possible to do the initial question?

- February 4th 2010, 04:07 AMCalculus26
No it is very possible though a little more difficult-- my impression is that at this level it would seem the one I suggested would be more relevant.

However for the original

| (x + 3)/(x-3)(x+3)| < |2x/(x+3)(x-3| since for x > 3 x + x > x+3

|2x/(x+3)(x-3)|< | 2x/(x)(x-3)| smaller denominator bigger fraction x < x+3

| 2x/(x)(x-3)| = 2/(x-3) x > 3

2/(x-3) < e

1/(x-3) < e/2

again if x- 3 > e/2

1/(x-3) < e/2

M = 3 + e/2