Consider the function y = f(x). Below is a table of values for the function f. %3D f(x) f(x) 2.1 1.1201 1.9 -1.1201 2.01 1.0256 1.99 -1.0256 2.001 1.0015 1.999 -1.0015 2.0001 1.0002 1.9999 -1.0002 Based on this table only, what is the best estimate for the limit lim f(x)? 2 -1 1 Does not exist None of the above
Consider the function y = f(x). Below is a table of values for the function f. %3D f(x) f(x) 2.1 1.1201 1.9 -1.1201 2.01 1.0256 1.99 -1.0256 2.001 1.0015 1.999 -1.0015 2.0001 1.0002 1.9999 -1.0002 Based on this table only, what is the best estimate for the limit lim f(x)? 2 -1 1 Does not exist None of the above
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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![Consider the function \( y = f(x) \). Below is a table of values for the function \( f \).
\[
\begin{array}{|c|c|c|c|}
\hline
x & f(x) & x & f(x) \\
\hline
2.1 & 1.1201 & 1.9 & -1.1201 \\
2.01 & 1.0256 & 1.99 & -1.0256 \\
2.001 & 1.0015 & 1.999 & -1.0015 \\
2.0001 & 1.0002 & 1.9999 & -1.0002 \\
\hline
\end{array}
\]
Based on this table only, what is the best estimate for the limit \(\lim_{x \to 2} f(x)\)?
- \( \bigcirc \) 2
- \( \bigcirc \) -1
- \( \bigcirc \) 1
- \( \bigcirc \) Does not exist
- \( \bigcirc \) None of the above
Explanation:
The table provides values of \( f(x) \) for \( x \) approaching 2 from both sides. As \( x \) approaches 2 from the right (e.g., 2.1, 2.01, 2.001, 2.0001), \( f(x) \) approaches 1. As \( x \) approaches 2 from the left (e.g., 1.9, 1.99, 1.999, 1.9999), \( f(x) \) approaches -1. Therefore, these values suggest different limits from the left and right, implying the limit does not exist.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86af8d60-5725-413a-bdf1-49ede3800267%2Fcdbbb1f1-5385-42f5-b53a-1428c0776ae2%2Fd7ox4v_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function \( y = f(x) \). Below is a table of values for the function \( f \).
\[
\begin{array}{|c|c|c|c|}
\hline
x & f(x) & x & f(x) \\
\hline
2.1 & 1.1201 & 1.9 & -1.1201 \\
2.01 & 1.0256 & 1.99 & -1.0256 \\
2.001 & 1.0015 & 1.999 & -1.0015 \\
2.0001 & 1.0002 & 1.9999 & -1.0002 \\
\hline
\end{array}
\]
Based on this table only, what is the best estimate for the limit \(\lim_{x \to 2} f(x)\)?
- \( \bigcirc \) 2
- \( \bigcirc \) -1
- \( \bigcirc \) 1
- \( \bigcirc \) Does not exist
- \( \bigcirc \) None of the above
Explanation:
The table provides values of \( f(x) \) for \( x \) approaching 2 from both sides. As \( x \) approaches 2 from the right (e.g., 2.1, 2.01, 2.001, 2.0001), \( f(x) \) approaches 1. As \( x \) approaches 2 from the left (e.g., 1.9, 1.99, 1.999, 1.9999), \( f(x) \) approaches -1. Therefore, these values suggest different limits from the left and right, implying the limit does not exist.
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