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I got a couple of question, hope I wont bother you guys too much.. its about function limits.

1)

http://www.upit.ws/uploads/53401353963d7.JPG

1. The problem statement, all variables and given/known data

what I tried to do was to say that for all delta>x-(7/4) there is 3x/(4x-7)>M

than I tried to work with 3x/(4x-7)>M so that ill get an expression that looks like x-(7/4) but I got stuck trying to get it out of the denominator.

2)

http://www.upit.ws/uploads/6e159c2fa9206.JPG

if to every epsilon>0 theres a x0 so that for all x > x0 exists |f(x) - L| > epsilon.

tried developing the |f(x) - L| > epsilon part but got stuck in: |(2x+7)/(x^2 +3x +1)| < epsilon

3)

for extra credit :) I need to prove (using epsilon and delta) that if a function has a limit (when x->infinity) then its singular, meaning if f(x) [x->infinity]=L and f(x) [x->infinity]=K then L=K !

I know it probably dosent seem like I tried too hard from the attempts to solution I wrote but I wasted quite a few pages on different tries. They just dont seem to get me anywhere so I saved me the trouble of trying to write them in english (not exactly my forte..)

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# Homework Help: Push to the limits

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