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"