Use the given graph of f(x) to evaluate each limit. If the limit does not exist, enter your answer as DNE -5 -4 -3 -2 -1 3 4 5 a.) lim f(x) = b.) lim f(x) = #11 c.) lim f(x) = 2-1 d.) lim f(x) = 4400 55 4 3 2 HY A -2 -3 -4 ܘ 1 2
Use the given graph of f(x) to evaluate each limit. If the limit does not exist, enter your answer as DNE -5 -4 -3 -2 -1 3 4 5 a.) lim f(x) = b.) lim f(x) = #11 c.) lim f(x) = 2-1 d.) lim f(x) = 4400 55 4 3 2 HY A -2 -3 -4 ܘ 1 2
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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### Evaluating Limits Using Graphs
**Instructions:** Use the given graph of \( f(x) \) to evaluate each limit. If the limit does not exist, enter your answer as DNE (Does Not Exist).
#### Graph Description
The graph consists of two main sections and a discontinuity at \( x = 1 \):
- For \( x < 1 \):
- The curve starts at \( y = 2 \) when \( x = -5 \) and continuously decreases in a smooth curve.
- As \( x \) approaches 1 from the left (\( x \to 1^- \)), the graph descends towards \( y = 1 \).
- For \( x > 1 \):
- The curve is discontinuous at \( x = 1 \) and resumes at \( x = 1 \) with an open circle at \( y = -3 \).
- The graph then steadily increases from \( y = -3 \) as \( x \) increases, approaching \( y = 2 \) as \( x \) goes to 5.
#### Limits to be Evaluated
**(a.)** \( \lim_{x \to 1} f(x) = \)
**(b.)** \( \lim_{x \to 1^-} f(x) = \)
**(c.)** \( \lim_{x \to 1^+} f(x) = \)
**(d.)** \( \lim_{x \to \infty} f(x) = \)
---
### Worked Examples
1. **Left-Hand Limit as \( x \) Approaches 1:**
- As \( x \) approaches 1 from the left-hand side (\( x \to 1^- \)), the function \( f(x) \) approaches 1.
\[
\lim_{x \to 1^-} f(x) = 1
\]
2. **Right-Hand Limit as \( x \) Approaches 1:**
- As \( x \) approaches 1 from the right-hand side (\( x \to 1^+ \)), the function \( f(x) \) approaches -3.
\[
\lim_{x \to 1^+} f(x) = -3
\]
3. **Two-Sided Limit as \( x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbc3f4f4-d793-4827-8e3d-2f51535d2e99%2F75933271-6921-4f6b-9d63-9fd9fac6527b%2F1ziwzup_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Evaluating Limits Using Graphs
**Instructions:** Use the given graph of \( f(x) \) to evaluate each limit. If the limit does not exist, enter your answer as DNE (Does Not Exist).
#### Graph Description
The graph consists of two main sections and a discontinuity at \( x = 1 \):
- For \( x < 1 \):
- The curve starts at \( y = 2 \) when \( x = -5 \) and continuously decreases in a smooth curve.
- As \( x \) approaches 1 from the left (\( x \to 1^- \)), the graph descends towards \( y = 1 \).
- For \( x > 1 \):
- The curve is discontinuous at \( x = 1 \) and resumes at \( x = 1 \) with an open circle at \( y = -3 \).
- The graph then steadily increases from \( y = -3 \) as \( x \) increases, approaching \( y = 2 \) as \( x \) goes to 5.
#### Limits to be Evaluated
**(a.)** \( \lim_{x \to 1} f(x) = \)
**(b.)** \( \lim_{x \to 1^-} f(x) = \)
**(c.)** \( \lim_{x \to 1^+} f(x) = \)
**(d.)** \( \lim_{x \to \infty} f(x) = \)
---
### Worked Examples
1. **Left-Hand Limit as \( x \) Approaches 1:**
- As \( x \) approaches 1 from the left-hand side (\( x \to 1^- \)), the function \( f(x) \) approaches 1.
\[
\lim_{x \to 1^-} f(x) = 1
\]
2. **Right-Hand Limit as \( x \) Approaches 1:**
- As \( x \) approaches 1 from the right-hand side (\( x \to 1^+ \)), the function \( f(x) \) approaches -3.
\[
\lim_{x \to 1^+} f(x) = -3
\]
3. **Two-Sided Limit as \( x
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