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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![### Exercises for Calculus Students
#### Exercise To Try 3
**Determine the limits:**
\[
\lim_{{x \to 1}} \frac{2 - x}{{(x - 1)^2}}
\]
#### Exercise To Try 4
**Let \( f(x) = \frac{x^2 - 25}{(x - 5)} \).**
**(a) Graph \( f(x) \).**
*Graph Description:*
An empty Cartesian coordinate system is provided with both the x-axis and y-axis labeled but unmarked with specific values. Students are expected to draw the graph of the function \( f(x) = \frac{x^2 - 25}{(x - 5)} \) onto this coordinate plane.
**(b) Find the limit:**
\[
\lim_{{x \to 5}} =
\]
**Instructions:**
For Exercise 3, calculate the limit as \( x \) approaches 1 for the given function.
For Exercise 4:
1. Simplify the function \( f(x) \) if possible, particularly considering factoring in the numerator \( x^2 - 25 \).
2. Draw the graph of the function \( f(x) = \frac{x^2 - 25}{(x - 5)} \) on the provided coordinate plane.
3. Determine the limit of \( f(x) \) as \( x \) approaches 5 and write the value in the space provided.
The emphasis in both exercises is on understanding and working with limits and graphing rational functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89524ea7-6be4-4cd1-8a76-e790f4380b75%2F25d25214-e027-4471-aeb5-29c673e64c18%2Fu3c6zn.png&w=3840&q=75)
Transcribed Image Text:### Exercises for Calculus Students
#### Exercise To Try 3
**Determine the limits:**
\[
\lim_{{x \to 1}} \frac{2 - x}{{(x - 1)^2}}
\]
#### Exercise To Try 4
**Let \( f(x) = \frac{x^2 - 25}{(x - 5)} \).**
**(a) Graph \( f(x) \).**
*Graph Description:*
An empty Cartesian coordinate system is provided with both the x-axis and y-axis labeled but unmarked with specific values. Students are expected to draw the graph of the function \( f(x) = \frac{x^2 - 25}{(x - 5)} \) onto this coordinate plane.
**(b) Find the limit:**
\[
\lim_{{x \to 5}} =
\]
**Instructions:**
For Exercise 3, calculate the limit as \( x \) approaches 1 for the given function.
For Exercise 4:
1. Simplify the function \( f(x) \) if possible, particularly considering factoring in the numerator \( x^2 - 25 \).
2. Draw the graph of the function \( f(x) = \frac{x^2 - 25}{(x - 5)} \) on the provided coordinate plane.
3. Determine the limit of \( f(x) \) as \( x \) approaches 5 and write the value in the space provided.
The emphasis in both exercises is on understanding and working with limits and graphing rational functions.
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