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Question
Find \[\lim_{x \to 3} f\left( x \right)\] where \[f\left( x \right) = \begin{cases}4, & if x > 3 \\ x + 1, & if x < 3\end{cases}\]
Solution
We have,
\[f\left( x \right) = \begin{cases}4, & if x > 3 \\ x + 1, & if x < 3\end{cases}\]
LHL of f(x) at x = 3
= \[\lim_{x \to 3^-} f\left( x \right) = \lim_{h \to 0} f\left( 3 - h \right) = \lim_{h \to 0} \left( 3 - h + 1 \right) = 4\]
RHL of f(x) at x = 3
= \[\lim_{x \to 3^+} f\left( x \right) = \lim_{h \to 0} f\left( 3 + h \right) = \lim_{h \to 0} 4 = 4\]
Clearly,
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