Use a graphing utility or spread-sheet software program to...

Name: Problem 22, Chapter 3: Calculus an Applied Approach
Uploaded: 2021-06-16T14:15:34-08:00
Duration: 1 min 8 s
Channel: Adrian Co
Description: Use a graphing utility or spread-sheet software program to complete the table. Then use the result to estimate the limit of f(x) as x approaches infinity. x 10^0 10^1 10^2 10^3 10^4 10^5 10^6 f(x) f(x)=(2 x^2)/(x+1)

Use a graphing utility or spread-sheet software program to complete the table. Then use the result to estimate the limit of $f(x)$ as $x$ approaches infinity. $$ \begin{array}{|c|c|c|c|c|c|c|c|}\hline x & {10^{0}} & {10^{1}} & {10^{2}} & {10^{3}} & {10^{4}} & {10^{5}} & {10^{6}} \\ \hline f(x) & {} & {} & {} & {} \\ \hline\end{array} $$ $$ f(x)=\frac{2 x^{2}}{x+1} $$

Use a graphing utility or spread-sheet software program to complete the table. Then use the result to estimate the limit of $f(x)$ as $x$ approaches infinity.
$$
\begin{array}{|c|c|c|c|c|c|c|c|}\hline x & {10^{0}} & {10^{1}} & {10^{2}} & {10^{3}} & {10^{4}} & {10^{5}} & {10^{6}} \\ \hline f(x) & {} & {} & {} & {} \\ \hline\end{array}
$$
$$
f(x)=\frac{2 x^{2}}{x+1}
$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Graphical Analysis and Data Estimation

Using graphing utilities or spreadsheet software to create tables of values is a practical method for estimating limits. This approach helps visualize the trend of the function as the variable increases and supports the analytical determination of the function’s end behavior.

Degree Comparison in Polynomials

For rational functions, the degrees of the numerator and denominator give insight into the function's behavior at extreme values. If the numerator's degree is higher than the denominator's, the function generally increases or decreases without bound as x approaches infinity.

Limit at Infinity

This concept involves understanding the behavior of a function as the variable grows without bound. It focuses on what value, if any, the function approaches as the input becomes very large (positively or negatively).

Rational Functions

Rational functions are fractions of polynomials. Analyzing their limits, especially as x approaches infinity, typically involves comparing the degrees of the polynomials in the numerator and denominator to determine end behavior.

Transcript

Please give Ace some feedback