Question

for any number epsilon > 0, if we can find an open interval (x0, x1 ) on the x-axis containing the point a such that
L - epsilon < f(x) < L + epsilon
for each x in ( x0, x1 ) except possibly x = a.
Then we can say,
lim f(x) = L
x-> a

so, f(x) is in the interval ( L - epsilon, L + epsilon )

i need explanation. don't worry i will get fast whatever u will tell me about that.

select my question to answer, I'm here i will livechat with the mentors.

Answer 1

yes,
x is in interval (x-delta, x+delta)

remember ( ) is parenthesis for open set, and [] for closed set, and also f(x) is within (L-epsilon, L + epsilon) an open set.