evaluate each of the following expressions. note: enter dne if the limit does not exist or is not defined…

evaluate each of the following expressions. note: enter dne if the limit does not exist or is not defined. a) $lim_{x\rightarrow - 1^{-}}f(x)=3$ b) $lim_{x\rightarrow - 1^{+}}f(x)=1$ c) $lim_{x\rightarrow - 1}f(x)=dne$ d) $f(-1)=0$ e) $lim_{x\rightarrow1^{-}}f(x)=0$ f) $lim_{x\rightarrow1^{+}}f(x)=6$ g) $lim_{x\rightarrow1}f(x)=dne$ h) $lim_{x\rightarrow3}f(x)=6$ i) $f(3)=6$

evaluate each of the following expressions. note: enter dne if the limit does not exist or is not defined. a) $lim_{x\rightarrow - 1^{-}}f(x)=3$ b) $lim_{x\rightarrow - 1^{+}}f(x)=1$ c) $lim_{x\rightarrow - 1}f(x)=dne$ d) $f(-1)=0$ e) $lim_{x\rightarrow1^{-}}f(x)=0$ f) $lim_{x\rightarrow1^{+}}f(x)=6$ g) $lim_{x\rightarrow1}f(x)=dne$ h) $lim_{x\rightarrow3}f(x)=6$ i) $f(3)=6$

Answer

Explanation:

Step1: Analyze left - hand limit as x→ - 1

As x approaches - 1 from the left side (x→ - 1⁻), by looking at the graph, the y - value approaches 3.

Step2: Analyze right - hand limit as x→ - 1

As x approaches - 1 from the right side (x→ - 1⁺), by looking at the graph, the y - value approaches 1. Since the left - hand limit and the right - hand limit are not equal, (\lim_{x\rightarrow - 1}F(x)) does not exist (DNE).

Step3: Find the value of F(-1)

The value of the function at x = - 1 is given by the y - coordinate of the point on the graph at x=-1, which is 0.

Step4: Analyze left - hand limit as x→1

As x approaches 1 from the left side (x→1⁻), by looking at the graph, the y - value approaches 0.

Step5: Analyze right - hand limit as x→1

As x approaches 1 from the right side (x→1⁺), by looking at the graph, the y - value approaches 6. Since the left - hand limit and the right - hand limit are not equal, (\lim_{x\rightarrow1}F(x)) does not exist (DNE).

Step6: Analyze limit as x→3

As x approaches 3, the graph approaches a y - value of 6, and also F(3) = 6.

Answer:

a. 3 b. 1 c. DNE d. 0 e. 0 f. 6 g. DNE h. 6 i. 6