Question

lim as x approches 0

( x^2, x<0)
(1+x, x>0)

decide if the limit exists.

Answer 1

Let me help you arrange it
find \(lim_{x\rightarrow}f(x)\) if it exists.
\[f(x) =\begin{cases}x^2~~~~~~if~~~~x<0\\1+x~~~~~~if~~~~x>0\end{cases}\]

Answer 2

@xapproachesinfinity hey kid, now your turn. :)

Answer 3

\[\large \lim_{x\to0}f(x)\text{ exists if }\\~\\~\\\large \text{both }\lim_{x\to0^-}f(x) \text{ and }\lim_{x\to0^+}f(x) \text{ exist}\\~\\~\\ \large\text{and }\lim_{x\to0^-}f(x)=\lim_{x\to0^+}f(x)\]