it does not seem,but I think it is a challenging problem. help me to solve it.

[fatemeh8989]

If for every x ϵ [a-ᵹ, a+ᵹ] – {a} f(x) ≥ b ,by the difinition of limit prove that lim f(x) (as x → a) is greater than(or equal to) b.
Discuss about it when the lim of f(x) at point x=a exist and when does not exist.
the way i tried is contrudiction method, so i supposed that lim f(x) as x-->a is L and L < b.
so - L > -b and f(x)- L > f(x) - b , l f(x) - L l >= l f(x) l - l L l so,
l f(x) l - l L l > l f(x) - b l
l f(x) l > lf(x) - b l + l L l...
i dont know what to do next... i was trying to get to something to be in conter with f(x)>b...
can you help me...
thank you!

 

[daon2]

Let a,b=0 for simplicity. If the limit were less than 0, then let epsilon = |L|. Let delta be such that 0<|x|<d => |f(x)-L| < |L|. Then 2L < f(x) < 0 for every x within delta of 0.