Question

give the value of each statement. if the value does not exist, write \dne\.
a) $lim_{x
ightarrow3}f(x)=$
b) $f(3)=$
c) $lim_{x
ightarrow1}f(x)=$
d) $f(1)=$

Explanation:

Step1: Analyze $\lim_{x

ightarrow3}f(x)$
As $x$ approaches 3 from the left and right, the function values approach 2. So $\lim_{x
ightarrow3}f(x)=2$.

Step2: Find $f(3)$

The open - circle at $x = 3$ means the function is not defined at $x=3$, so $f(3)=\text{DNE}$.

Step3: Analyze $\lim_{x

ightarrow1}f(x)$
As $x$ approaches 1 from the left and right, the function values approach 4. So $\lim_{x
ightarrow1}f(x)=4$.

Step4: Find $f(1)$

The closed - circle at $x = 1$ indicates that $f(1)=2$.

Answer:

a) 2
b) DNE
c) 4
d) 2