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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Hi I am really stuck on question 46 for my homework I am pretty lost. We are supposed to write a simpler function that agrees with the given funtion at all but one point and also find the limit of the function.
![### Chapter 1: Limits and Their Properties
#### Practice Exercises
This section provides various exercises focusing on finding limits. Each exercise represents specific types of functions to practice and understand the concepts surrounding limits.
---
**Exercises 11-22: Finding Limits**
1. \(\lim_{{x \to 0}} \frac{x^2 + 4x + 1}{x}\)
2. \(\lim_{{x \to 1}} \frac{x}{x + 8}\)
3. \(\lim_{{x \to 3}} (x^3)\)
4. \(\lim_{{x \to 1}} \frac{3x}{2x + 1}\)
5. \(\lim_{{x \to -2}} (x + 1)\)
6. \(\lim_{{x \to 1}} \frac{x^2 + 3}{x + 1}\)
7. \(\lim_{{x \to 0}} \frac{x^2}{3x + 2}\)
8. \(\lim_{{x \to \infty}} (3x^2 + 2)\)
9. \(\lim_{{x \to 1}} \frac{x^4 - 1}{x - 1}\)
10. \(\lim_{{x \to \infty}} (2 + \frac{1}{x})\)
11. \(\lim_{{x \to -2}} (x + 4)\)
12. \(\lim_{{x \to \infty}} \sqrt{(2x + 3)}\)
13. \(\lim_{{x \to 1}} \sqrt[3]{(x^2 + 1)}\)
14. \(\lim_{{x \to \infty}} (2x^2+1)\)
15. \(\lim_{{x \to 0}} \frac{3x^3 + 2}{2x + 1}\)
16. \(\lim_{{x \to 1}} \frac{x^4 - x^2}{x^3 + x^2}\)
17. \(\lim_{{x \to 1}} \frac{3x^3 + 2x^2}{x^3 - 1}\)
18. \(\lim](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ffb9870-2903-4965-9b25-0c5e2f1ebec2%2F6e822b7d-d62a-445e-af2a-e212109f9ce2%2Febok88c.png&w=3840&q=75)
Transcribed Image Text:### Chapter 1: Limits and Their Properties
#### Practice Exercises
This section provides various exercises focusing on finding limits. Each exercise represents specific types of functions to practice and understand the concepts surrounding limits.
---
**Exercises 11-22: Finding Limits**
1. \(\lim_{{x \to 0}} \frac{x^2 + 4x + 1}{x}\)
2. \(\lim_{{x \to 1}} \frac{x}{x + 8}\)
3. \(\lim_{{x \to 3}} (x^3)\)
4. \(\lim_{{x \to 1}} \frac{3x}{2x + 1}\)
5. \(\lim_{{x \to -2}} (x + 1)\)
6. \(\lim_{{x \to 1}} \frac{x^2 + 3}{x + 1}\)
7. \(\lim_{{x \to 0}} \frac{x^2}{3x + 2}\)
8. \(\lim_{{x \to \infty}} (3x^2 + 2)\)
9. \(\lim_{{x \to 1}} \frac{x^4 - 1}{x - 1}\)
10. \(\lim_{{x \to \infty}} (2 + \frac{1}{x})\)
11. \(\lim_{{x \to -2}} (x + 4)\)
12. \(\lim_{{x \to \infty}} \sqrt{(2x + 3)}\)
13. \(\lim_{{x \to 1}} \sqrt[3]{(x^2 + 1)}\)
14. \(\lim_{{x \to \infty}} (2x^2+1)\)
15. \(\lim_{{x \to 0}} \frac{3x^3 + 2}{2x + 1}\)
16. \(\lim_{{x \to 1}} \frac{x^4 - x^2}{x^3 + x^2}\)
17. \(\lim_{{x \to 1}} \frac{3x^3 + 2x^2}{x^3 - 1}\)
18. \(\lim
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