Questions: Homework: Assignment 1.1 - Introduction to Question 8, 2.2.17 Limits Part 3 of 12 Use the graph of to complete parts (a) through (1). If a limit does not exist, explain why. (a) Find f(1). Select the correct choice below, and fill in the answer box if necessary. f(1)=3 (Type an integer or a fraction.) B. The value of f(1) is undefined. (b) Find lim x -> 1^- f(x). Select the correct choice below, and fill in the answer box if necessary. A. lim x -> 1^- f(x)=2 (Type an integer or a fraction.) B. The limit does not exist because f(x) is not defined for all x<1. (c) Find lim x -> 1^+ f(x). Select the correct choice below, and fill in the answer box if necessary. A. lim x -> 1^+ f(x)= (Type an integer or a fraction.) B. The limit does not exist because f(x) is not defined for all x>1.

Homework: Assignment 1.1 - Introduction to Question 8, 2.2.17 Limits Part 3 of 12 Use the graph of to complete parts (a) through (1). If a limit does not exist, explain why. (a) Find f(1). Select the correct choice below, and fill in the answer box if necessary. f(1)=3 (Type an integer or a fraction.) B. The value of f(1) is undefined. (b) Find lim x -> 1^- f(x). Select the correct choice below, and fill in the answer box if necessary. A. lim x -> 1^- f(x)=2 (Type an integer or a fraction.) B. The limit does not exist because f(x) is not defined for all x<1. (c) Find lim x -> 1^+ f(x). Select the correct choice below, and fill in the answer box if necessary. A. lim x -> 1^+ f(x)= (Type an integer or a fraction.) B. The limit does not exist because f(x) is not defined for all x>1.
Transcript text: Homework: Assignment 1.1 - Introduction to Question 8, 2.2.17 Limits Part 3 of 12 Use the graph of to complete parts (a) through (1). If a limit does not exist, explain why. (a) Find $\mathrm{f}(1)$. Select the correct choice below, and fill in the answer box if necessary. $f(1)=3$ (Type an integer or a fraction.) B. The value of $f(1)$ is undefined. (b) Find $\lim _{x \rightarrow 1^{-}} f(x)$. Select the correct choice below, and fill in the answer box if necessary. A. $\lim _{x \rightarrow 1^{-}} f(x)=2$ (Type an integer or a fraction.) B. The limit does not exist because $f(x)$ is not defined for all $x<1$. (c) Find $\lim _{x \rightarrow 1^{+}} f(x)$. Select the correct choice below, and fill in the answer box if necessary. A. $\lim _{x \rightarrow 1^{+}} f(x)=$ $\square$ (Type an integer or a fraction.) B. The limit does not exist because $\mathrm{f}(\mathrm{x})$ is not defined for all $\mathrm{x}>1$.
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Solution

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(a) Find \( f(1) \). Select the correct choice below, and fill in the answer box if necessary.

Evaluate \( f(1) \) from the graph.

From the graph, \( f(1) = 3 \).

\\(\boxed{f(1) = 3}\\)

(b) Find \( \lim _{x \rightarrow 1^{-}} f(x) \). Select the correct choice below, and fill in the answer box if necessary.

Evaluate the left-hand limit as \( x \) approaches 1.

From the graph, as \( x \) approaches 1 from the left, \( f(x) \) approaches 2.

\\(\boxed{\lim _{x \rightarrow 1^{-}} f(x) = 2}\\)

(c) Find \( \lim _{x \rightarrow 1^{+}} f(x) \). Select the correct choice below, and fill in the answer box if necessary.

Evaluate the right-hand limit as \( x \) approaches 1.

From the graph, as \( x \) approaches 1 from the right, \( f(x) \) approaches 4.

\\(\boxed{\lim _{x \rightarrow 1^{+}} f(x) = 4}\\)

\\(\boxed{f(1) = 3}\\)
\\(\boxed{\lim _{x \rightarrow 1^{-}} f(x) = 2}\\)
\\(\boxed{\lim _{x \rightarrow 1^{+}} f(x) = 4}\\)

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