$$\lim _ { x \rightarrow 3 ^ {- } } f ( x ) = 3$$ where $$f ( x ) = \left\{ \begin{aligned}
x & \text { if } x

Name: \[\lim _ { x \rightarrow 3 ^ {- } } f ( x ) = 3\] where \[f ( x ) = \left\{ \begin{aligned} x & \text { if } x < 3 \\ x + 1 & \text { if } x \geq 3 \end{aligned} \right.\]
Brand: Quizplus
Rating: 4.8 (37 reviews)

Question

$$\lim _ { x \rightarrow 3 ^ {- } } f ( x ) = 3$$ where $$f ( x ) = \left\{ \begin{aligned}
x & \text { if } x < 3 \
x + 1 & \text { if } x \geq 3
\end{aligned} \right.$$

Quizplus · Accepted Answer

As $x$ approaches 3 from the left ($x \rightarrow 3^-$), the function $f(x) = x$ for $x < 3$, so the limit is equal to 3.

lim⁡x→3−f(x)=3\lim _ { x \rightarrow 3 ^ {- } } f ( x ) = 3x→3−lim​f(x)=3

$\lim _ { x \rightarrow 3 ^ {- } } f ( x ) = 3$