Epsilon/delta?
Find and prove using the epsilon/delta definition:
\lim _{x\to 1}\(3x^2-4)
Find and prove using the epsilon/delta definition:
2 Answers
To prove it we choose arbitrarily
Note now that:
and, if
so,
Then if for any
which proves the point.
Please see below.
Explanation:
Claim:
For
Observe that if
Furthermore, (for
= 3abs(x^2-1)
= 3abs(x-1)abs(x+1)
< 3(delta)(3)
= 9(epsilon/9)
= epsilon