Question

find each indicated quantity if it exists. let f(x) = { x^2, for x < - 2; 2x, for x > - 2 }. 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→ - 2^+} f(x) = (type an integer.) b. the limit does not exist.

Explanation:

Step1: Identify the function for right - hand limit

For $\lim_{x
ightarrow - 2^{+}}f(x)$, since $x
ightarrow - 2^{+}$ means $x > - 2$, the function is $f(x)=2x$.

Step2: Substitute the value of $x$

Substitute $x=-2$ into $f(x) = 2x$. We get $2\times(-2)=-4$.

Answer:

A. $\lim_{x
ightarrow - 2^{+}}f(x)=-4$