Find limx→0 f(x) and limx→0 f(x) where f(n) {(2x +3), x≤0 3(x+1), x>0

Question

Find lim_x→0 f(x) and lim_x→0 f(x) where

\(f(x) = \begin{cases} 2x + 3 & x\leq0 \\ 3(x+1), & x>0 \end{cases}\)

Answer 1

\(\lim\limits_{x \to 0^-}\) f(x) = \(\lim\limits_{x \to 0}\)(2x + 3) = 3

\(\lim\limits_{x \to {0^+}}\) f(x) = \(\lim\limits_{x \to 0}\)3(x +1) = 3

Therefore; \(\lim\limits_{x \to 0}\) f(x) = 3

\(\lim\limits_{x \to 1}\) f(x) = \(\lim\limits_{x \to 1}\) 3(x+1) = 3 x 2 = 6