Complete the table. (Round your answers to four decimal places. Assume x is in terms of radian.) 4 cos(x) lim - 4 -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x) .1998 0.0200 0.002 -0.002 -.02 -.1998 Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to four decimal places.) 4 cos(x) – 4 lim 2 0.006 Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers four decimal places. If an answer does not exist, enter DNE.) x - 6 lim I+1 x2 - 4r – 12 0.9 0.99 0.999 1.001 1.01 1.1 f(x) .3448 3344 .3334 .3332 .3322 .3226 lim I+1 r - 4.r – 12 z Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal plac an answer does not exist, enter DNE.) 45 - x - 7 lim X-4 X + 4 -4.1 -4.01 -4.001 -3.999 -3.99 -3.9 f(x) -0.0714 -0.0714 |-0.0714 |-0.0714 -0.0714 -0.0715 4) V 45 - x - 7 lim x-4 x + 4
Complete the table. (Round your answers to four decimal places. Assume x is in terms of radian.) 4 cos(x) lim - 4 -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x) .1998 0.0200 0.002 -0.002 -.02 -.1998 Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to four decimal places.) 4 cos(x) – 4 lim 2 0.006 Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers four decimal places. If an answer does not exist, enter DNE.) x - 6 lim I+1 x2 - 4r – 12 0.9 0.99 0.999 1.001 1.01 1.1 f(x) .3448 3344 .3334 .3332 .3322 .3226 lim I+1 r - 4.r – 12 z Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal plac an answer does not exist, enter DNE.) 45 - x - 7 lim X-4 X + 4 -4.1 -4.01 -4.001 -3.999 -3.99 -3.9 f(x) -0.0714 -0.0714 |-0.0714 |-0.0714 -0.0714 -0.0715 4) V 45 - x - 7 lim x-4 x + 4
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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I have circled in purple my question in the attached .jpg parts A, B, and C
please and thank you
![### Evaluating Limits: Step-by-Step Guide
This educational page will guide students through evaluating limits by completing numerical tables, estimating limits, and utilizing graphing tools.
---
#### 1. Completing the Table
Complete the table. (Round your answers to four decimal places. Assume \( x \) is in terms of radians.)
\[
\lim_{{x \to 0}} \frac{4 \cos(x) - 4}{x}
\]
| \( x \) | -0.1 | -0.01 | -0.001 | 0 | 0.001 | 0.01 | 0.1 |
|-----------|--------|--------|--------|--------|-------|-------|--------|
| \( f(x) \)| 0.1998 | 0.0200 | 0.002 | ? | -0.002| -0.02 | -0.1998|
To fill in the value at \( x = 0 \):
\[
\frac{4 \cos(0) - 4}{0} = \frac{4 \cdot 1 - 4}{0} = \frac{0}{0} \quad \text{(Indeterminate form)}
\]
Thus, \( \lim_{{x \to 0}} \frac{4 \cos(x) - 4}{x} \) requires further analysis.
Use the table's data as a guide for the limit:
- \( f(x) \) values are getting closer to 0 as \( x \) approaches 0.
#### 2. Estimating the Limit
Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to four decimal places.)
\[
\lim_{{x \to 0}} \frac{4 \cos(x) - 4}{x} \approx 0.006
\]
#### 3. Table of Values for Another Function
Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal places. If an answer does not exist, enter DNE.)
\[
\lim_{{x \to 1}} \frac{x - 6}{x^2 - 4x -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb782184-6f8e-46f4-87c6-c110d703ce98%2Fdedfd9a7-1815-4fe7-aeb6-3857852ffcc0%2Fk8lbv2.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluating Limits: Step-by-Step Guide
This educational page will guide students through evaluating limits by completing numerical tables, estimating limits, and utilizing graphing tools.
---
#### 1. Completing the Table
Complete the table. (Round your answers to four decimal places. Assume \( x \) is in terms of radians.)
\[
\lim_{{x \to 0}} \frac{4 \cos(x) - 4}{x}
\]
| \( x \) | -0.1 | -0.01 | -0.001 | 0 | 0.001 | 0.01 | 0.1 |
|-----------|--------|--------|--------|--------|-------|-------|--------|
| \( f(x) \)| 0.1998 | 0.0200 | 0.002 | ? | -0.002| -0.02 | -0.1998|
To fill in the value at \( x = 0 \):
\[
\frac{4 \cos(0) - 4}{0} = \frac{4 \cdot 1 - 4}{0} = \frac{0}{0} \quad \text{(Indeterminate form)}
\]
Thus, \( \lim_{{x \to 0}} \frac{4 \cos(x) - 4}{x} \) requires further analysis.
Use the table's data as a guide for the limit:
- \( f(x) \) values are getting closer to 0 as \( x \) approaches 0.
#### 2. Estimating the Limit
Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to four decimal places.)
\[
\lim_{{x \to 0}} \frac{4 \cos(x) - 4}{x} \approx 0.006
\]
#### 3. Table of Values for Another Function
Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal places. If an answer does not exist, enter DNE.)
\[
\lim_{{x \to 1}} \frac{x - 6}{x^2 - 4x -
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