Question

enter each answer as a whole number (like -4, 0, or 253) or dne for undefined or does not exist.
f(6)=
lim_{x\to7^{-}} f(x)=
lim_{x\to0^{+}} f(x)=
lim_{x\to3} f(x)=
question help: video 1 video 2

Explanation:

Step1: Find f(6)

Locate x = 6 on the x - axis. The open - circle at (6, 1) is not part of the function, and the closed - circle at (6, 2) is part of the function. So f(6)=2.

Step2: Find $\lim_{x

ightarrow7^{-}}f(x)$
As x approaches 7 from the left, we look at the values of the function as x gets closer to 7 from values less than 7. The function approaches 6. So $\lim_{x
ightarrow7^{-}}f(x)=6$.

Step3: Find $\lim_{x

ightarrow0^{+}}f(x)$
As x approaches 0 from the right, we look at the values of the function as x gets closer to 0 from values greater than 0. The function approaches 4. So $\lim_{x
ightarrow0^{+}}f(x)=4$.

Step4: Find $\lim_{x

ightarrow3}f(x)$
As x approaches 3, the left - hand limit and the right - hand limit are not equal. The left - hand limit as x approaches 3 is 3 and the right - hand limit as x approaches 3 is 2. So $\lim_{x
ightarrow3}f(x)$ DNE.

Answer:

f(6) = 2
$\lim_{x
ightarrow7^{-}}f(x)=6$
$\lim_{x
ightarrow0^{+}}f(x)=4$
$\lim_{x
ightarrow3}f(x)$ DNE