Question

In Exercises 9-16, complete the table by computing $f(x)$ at the given values of $x$. Use these results to estimate the indicated limit (if it exists). $$ \begin{array}{l} f(x)=x^{2}+1 ; \lim _{x \rightarrow 2} f(x) \\ \hline x \quad 1.9 \quad 1.99 \quad 1.999 \quad 2.001 \quad 2.01 \quad 2.1 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & & & & & & \\ \hline \end{array} $$

Name: Problem 9, Chapter 9: Applied Mathematics: For the Managerial, Life, and Social Sciences
Uploaded: 2021-07-06T17:42:43-08:00
Duration: 1 min 21 s
Channel: Carson Merrill
Description: In Exercises 9-16, complete the table by computing f(x) at the given values of x. Use these results to estimate the indicated limit (if it exists). f(x)=x^2+1 ; limx → 2 f(x) x 1.9 1.99 1.999 2.001 2.01 2.1 f(x)

   In Exercises 9-16, complete the table by computing $f(x)$ at the given values of $x$. Use these results to estimate the indicated limit (if it exists).
$$
\begin{array}{l}
f(x)=x^{2}+1 ; \lim _{x \rightarrow 2} f(x) \\
\hline x \quad 1.9 \quad 1.99 \quad 1.999 \quad 2.001 \quad 2.01 \quad 2.1 \\
\hline \boldsymbol{f}(\boldsymbol{x}) & & & & & & \\
\hline
\end{array}
$$

Applied Mathematics: For the Managerial, Life, and Social Sciences

Soo T. Tan 5th Edition

Chapter 9, Problem 9

Instant Answer

Solved by Expert Carson Merrill

07/06/2021

Step 1

For $x = 1.9$, we have $f(1.9) = (1.9)^2 + 1 = 3.61 + 1 = 4.61$. For $x = 1.99$, we have $f(1.99) = (1.99)^2 + 1 = 3.9601 + 1 = 4.9601$. For $x = 1.999$, we have $f(1.999) = (1.999)^2 + 1 = 3.996001 + 1 = 4.996001$. For $x = 2.001$, we have $f(2.001) = Show more…

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In Exercises 9-16, complete the table by computing $f(x)$ at the given values of $x$. Use these results to estimate the indicated limit (if it exists). $$ \begin{array}{l} f(x)=x^{2}+1 ; \lim _{x \rightarrow 2} f(x) \\ \hline x \quad 1.9 \quad 1.99 \quad 1.999 \quad 2.001 \quad 2.01 \quad 2.1 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & & & & & & \\ \hline \end{array} $$

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Key Concepts

Limit

A limit describes the value that a function approaches as its input approaches a specific value. It is fundamental in calculus for understanding the behavior of functions at points where they may not be explicitly defined or where direct substitution leads to indeterminate forms.

Function Evaluation

This is the process of substituting specific values into a function to compute the corresponding output. It is a critical tool in verifying the behavior of functions near points of interest and in estimating limits.

Continuity

Continuity is the property of a function where small changes in the input result in small changes in the output. A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point, ensuring no discontinuities or jumps in the graph.

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