Are you allowed to use the formal definition of a limit to prove , and in doing so disprove ?
Hello
I'm having a lot of trouble with this proof:
Prove that the limit of f(x) = (x+1)/3 as x approaches 1 is NOT 2/3 + 10^-100
I've tried using the definition of the limit with epsilon as 10^-100/2 to get to a contradiction, but somehow it's not working out...any help would be greatly appreciated.
Which "bound x"? As we saw, x has to be greater than 1.0000.........02 (100 zeroes) in order to fulfil the requirement of
the limit's definition. But for any positive delta, there will be values of x s.t. |x - 1|
is less than the above
value and, thus, the abs. value...etc won't be less than that epsilon...
Tonio
Okay, I think I see...in order for the requirement to be fulfilled, x must be greater than 1.0000...02, but no matter what positive delta is given, there will always be values of x that both fulfill |x-1| < delta and x < 1.0000....002, in other words there will always be values at which the function is more than a distance of epsilon away from 2/3+10^-100.