12.2 The Concept of Limit

Solved Examples

LHL ( $x \to 0^-$ ): For $x < 0$ , $f(x) = x - 2$ . $\lim_{x \to 0^-} (x - 2) = 0 - 2 = -2$ .
RHL ( $x \to 0^+$ ): For $x > 0$ , $f(x) = x + 2$ . $\lim_{x \to 0^+} (x + 2) = 0 + 2 = +2$ .
Conclusion: Since LHL $\neq$ RHL ( $-2 \neq 2$ ), the limit does not exist.

Interactive Solver