Question

find each indicated quantity if it exists. let $f(x)=\begin{cases}x^{2},& \text{for }x < - 1\\-2x,& \text{for }x > - 1end{cases}$. complete parts (a) through (d). (a) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $lim_{x
ightarrow - 1^{+}}f(x)=\text{ (type an integer.)}$ b. the limit does not exist

Explanation:

Step1: Analyze left - hand limit

We want to find $\lim_{x
ightarrow - 1^{+}}f(x)$. Since $x
ightarrow - 1^{+}$ means $x > - 1$, we use the function $f(x)=-2x$.

Step2: Substitute the value

Substitute $x = - 1$ into $y=-2x$. We get $y=-2\times(-1)$.

Answer:

A. $\lim_{x
ightarrow - 1^{+}}f(x)=2$