Title: Understanding Limits Through Graphical Analysis---**Graph Analysis and Limits Matching Activity**Below is the graph of a function $ f $ depicted in the xy-plane. The graph provides a representation of how $ f(x) $ behaves as $ x $ varies.**Graph Description:**- The graph is plotted on a cartesian plane.- The x-axis ranges from 0 to 6, and the y-axis ranges from 0 to 6.- The graph shows a function starting from $ (0,1) $, dips to a minimum at around $ x=2 $ and then increases as $ x $ continues to 6.- There is an open circle at $ (1,1) $ indicating a hole (undefined point).- The graph passes through the points (2,1) and increases afterwards.**Task:**The task is to determine which of the given limits have equal values based on the graph provided.Select all that apply from the options below.**Options:**- $\ square \ \lim_{{x \to 1^-}} f(x) $- $\ square \ \lim_{{x \to 1^+}} f(x) $- $\ square \ \lim_{{x \to 1}} f(x) $- $\ square \ \lim_{{x \to 3^-}} f(x) $- $\ square \ \lim_{{x \to 3^+}} f(x) $- $\ square \ \lim_{{x \to 3}} f(x) $---By analyzing the graph, you'll be able to determine which limits have equal values. Remember that a limit exists where the function approaches a particular value as $ x $ approaches from either side (left or right).This exercise is instrumental in understanding the concepts of limits in calculus and recognizing the behavior of functions graphically.**Select all that apply and justify your choices based on the graphical properties of the function $ f $.**---

Answered: Image /qna-images/answer/63d2c5e2-1790-44aa-81d0-3c3018628496.jpg

Answered: 123456 The graph of the function fs…

123456 The graph of the function fs shown in the ry-plane above. Of the following, which limits have equal values? Select all that apply. O lim /(3) lim f) O tim f(x) O lim f(x) lim f(x) O lim f(x)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Title: Understanding Limits Through Graphical Analysis

---

**Graph Analysis and Limits Matching Activity**

Below is the graph of a function $ f $ depicted in the xy-plane. The graph provides a representation of how $ f(x) $ behaves as $ x $ varies.

**Graph Description:**

- The graph is plotted on a cartesian plane.
- The x-axis ranges from 0 to 6, and the y-axis ranges from 0 to 6.
- The graph shows a function starting from $ (0,1) $, dips to a minimum at around $ x=2 $ and then increases as $ x $ continues to 6.
- There is an open circle at $ (1,1) $ indicating a hole (undefined point).
- The graph passes through the points (2,1) and increases afterwards.

**Task:**

The task is to determine which of the given limits have equal values based on the graph provided.

Select all that apply from the options below.

**Options:**

- $\ square \ \lim_{{x \to 1^-}} f(x) $
- $\ square \ \lim_{{x \to 1^+}} f(x) $
- $\ square \ \lim_{{x \to 1}} f(x) $
- $\ square \ \lim_{{x \to 3^-}} f(x) $
- $\ square \ \lim_{{x \to 3^+}} f(x) $
- $\ square \ \lim_{{x \to 3}} f(x) $

---

By analyzing the graph, you'll be able to determine which limits have equal values. Remember that a limit exists where the function approaches a particular value as $ x $ approaches from either side (left or right).

This exercise is instrumental in understanding the concepts of limits in calculus and recognizing the behavior of functions graphically.

**Select all that apply and justify your choices based on the graphical properties of the function $ f $.**

---

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