Given,
f(x) = {2x+3, x ≤ 0 3(x+1),x < 0
(i)To find : lim f(x), x∈0
To limit to exist, we know
Thus to find the limit using the concept,
From above equations,
Thus the limit exists.
Thus from (5),
\(\lim\limits_{x \to 0}\) f(x) = 3
(ii) To find : lim f(x), x∈1
To limit to exist, we know
Thus to find the limit using the concept,
From above equations,
\(\lim\limits_{x \to 1^+}\) f(x) = \(\lim\limits_{x \to 1^-}\)f(x)
Thus from (2),(3) and (4),
\(\lim\limits_{x \to 1}\) f(x) = 5
