Find each function value and the limit for f(x) = 14-8x Use - co or co where appropriate. 3+x3 (A) f(- 10) (B) f(- 20) (C) lim f(x) xー→- 00 (A) f(- 10) = (Round to the nearest thousandth as needed.) (B) f(-20) =| nt (Round to the nearest thousandth as needed.) SS (C) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 14-8x3 lim O A. 3+x3 ri B. The limit does not exist and is neither - o nor co.
Find each function value and the limit for f(x) = 14-8x Use - co or co where appropriate. 3+x3 (A) f(- 10) (B) f(- 20) (C) lim f(x) xー→- 00 (A) f(- 10) = (Round to the nearest thousandth as needed.) (B) f(-20) =| nt (Round to the nearest thousandth as needed.) SS (C) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 14-8x3 lim O A. 3+x3 ri B. The limit does not exist and is neither - o nor co.
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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![### Function Evaluation and Limit Calculation
#### Problem Statement:
Given the function:
\[ f(x) = \frac{14 - 8x^3}{3 + x^3} \]
perform the following tasks:
1. **Find each function value and the limit for \( f(x) \). Use \( -\infty \) or \( \infty \) where appropriate.**
- (A) \( f(-10) \)
- (B) \( f(-20) \)
- (C) Evaluate the limit: \(\lim_{{x \to -\infty}} \frac{{14 - 8x^3}}{{3 + x^3}}\)
#### Instructions:
- Round all answers to the nearest thousandth as needed.
- For each evaluation, substitute the given x-values into the function and simplify.
- For the limit evaluation, determine the behavior of the function as \( x \) approaches \( -\infty \).
#### Questions:
(A) \( f(-10) = \) [ ]
(Round to the nearest thousandth as needed.)
(B) \( f(-20) = \) [ ]
(Round to the nearest thousandth as needed.)
(C) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- \( \lim_{{x \to -\infty}} \frac{{14 - 8x^3}}{{3 + x^3}} = \) [ ]
- The limit does not exist and is neither \( -\infty \) nor \( \infty \).
---
### Instructions to Input Responses:
1. **Function Evaluation:**
For (A) and (B), input the values of x into the function \( f(x) \) and calculate the results. Round your answers to the nearest thousandth.
- For \( f(-10) \), substitute \(-10\) into \( f(x) \).
- For \( f(-20) \), substitute \(-20\) into \( f(x) \).
2. **Limit Evaluation:**
Determine the end behavior of the function as \( x \) approaches \( -\infty \).
---
Click to select your answer(s).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5403b22d-6bfd-443b-9939-b04fac993812%2Fc7804e46-93ed-4bd0-84f1-1cb2399ce848%2Fl5vmrll_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Function Evaluation and Limit Calculation
#### Problem Statement:
Given the function:
\[ f(x) = \frac{14 - 8x^3}{3 + x^3} \]
perform the following tasks:
1. **Find each function value and the limit for \( f(x) \). Use \( -\infty \) or \( \infty \) where appropriate.**
- (A) \( f(-10) \)
- (B) \( f(-20) \)
- (C) Evaluate the limit: \(\lim_{{x \to -\infty}} \frac{{14 - 8x^3}}{{3 + x^3}}\)
#### Instructions:
- Round all answers to the nearest thousandth as needed.
- For each evaluation, substitute the given x-values into the function and simplify.
- For the limit evaluation, determine the behavior of the function as \( x \) approaches \( -\infty \).
#### Questions:
(A) \( f(-10) = \) [ ]
(Round to the nearest thousandth as needed.)
(B) \( f(-20) = \) [ ]
(Round to the nearest thousandth as needed.)
(C) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- \( \lim_{{x \to -\infty}} \frac{{14 - 8x^3}}{{3 + x^3}} = \) [ ]
- The limit does not exist and is neither \( -\infty \) nor \( \infty \).
---
### Instructions to Input Responses:
1. **Function Evaluation:**
For (A) and (B), input the values of x into the function \( f(x) \) and calculate the results. Round your answers to the nearest thousandth.
- For \( f(-10) \), substitute \(-10\) into \( f(x) \).
- For \( f(-20) \), substitute \(-20\) into \( f(x) \).
2. **Limit Evaluation:**
Determine the end behavior of the function as \( x \) approaches \( -\infty \).
---
Click to select your answer(s).
![### Calculus Problem: Finding Limits
#### Problem Statement
**Find**
\[ \lim_{{h \to 0}} \frac{{f(4 + h) - f(4)}}{h} \]
**if** \( f(x) = x^2 + 4 \).
---
\[ \lim_{{h \to 0}} \frac{{f(4 + h) - f(4)}}{h} \overset{\wedge}{=} \]
(Simplify your answer.)
---
**Instruction:**
Enter your answer in the answer box.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5403b22d-6bfd-443b-9939-b04fac993812%2Fc7804e46-93ed-4bd0-84f1-1cb2399ce848%2Fzoh4tpg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Problem: Finding Limits
#### Problem Statement
**Find**
\[ \lim_{{h \to 0}} \frac{{f(4 + h) - f(4)}}{h} \]
**if** \( f(x) = x^2 + 4 \).
---
\[ \lim_{{h \to 0}} \frac{{f(4 + h) - f(4)}}{h} \overset{\wedge}{=} \]
(Simplify your answer.)
---
**Instruction:**
Enter your answer in the answer box.
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