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**ah-bee** so im supposed to prove that x^2-7 is continuous at x=1

f(1) = -6

and now i need to use the formal definition to prove this.

so suppose |x-1|<delta, we need to deduce |x^2-1|<epsilon

i tried finding a delta that may satisfy this condition by working backwards, eg. trying to go from |x^2-1|<epsilon to |x-1|<'something'

and then letting delta equal that 'something' (note that working backwards is just a scrap piece of working, once i obtain the delta, i will say, suppose delta =.... and then continue with the proof). is there an easier approach to this or what, coz i dont wanna keep working backwards, which will be hard if i get a nasty function. or i could guess what delta is.. which is still a pain unless there is a systematic way of "guessing"