Find the limit (if it exists). $\lim _ { x \rightarrow 1 ^ { - } } f ( x )$, where $f ( x ) = \left\{ \begin{array} { c c } x ^ { 3 } + 10 , & x

Question

Find the limit (if it exists). $\lim _ { x \rightarrow 1 ^ { - } } f ( x )$, where $f ( x ) = \left\{ \begin{array} { c c } x ^ { 3 } + 10 , & x < 1 \ x + 10 , & x \geq 1 \end{array} \right.$
A) Limit does not exist.
B) 0
C) 10
D) 11
E) 30

Quizplus · Accepted Answer

To find the limit as $x$ approaches 1 from the left ($1^-$), we use the piece of the function defined for $x < 1$, which is $x^3 + 10$. Substituting $x = 1$ into this expression gives $1^3 + 10 = 11$.

Find the Limit (If It Exists) lim⁡x→1−f(x)\lim _ { x \rightarrow 1 ^ { - } } f ( x )limx→1−​f(x)

Find the Limit (If It Exists) $\lim _ { x \rightarrow 1 ^ { - } } f ( x )$