Question

use the graph to find the following limits and function value.
a. lim f(x) as x→0−
b. lim f(x) as x→0+
c. lim f(x) as x→0
d. f(0)
a. find the limit. select the correct choice below and fill in any answer boxes in your choice
a. lim f(x) as x→0− = (type an integer.)
b. the limit does not exist.

Explanation:

Step1: Analyze left - hand limit

As $x\to0^{-}$, the function approaches $0$.

Step2: Analyze right - hand limit

As $x\to0^{+}$, the function approaches $0$.

Step3: Analyze overall limit

Since left - hand and right - hand limits are equal, $\lim_{x\to0}f(x) = 0$.

Step4: Find function value

$f(0)=1$.

Answer:

a. A. $\lim_{x\to0^{-}}f(x)=0$
b. $\lim_{x\to0^{+}}f(x)=0$
c. $\lim_{x\to0}f(x)=0$
d. $f(0)=1$