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AP Calculus BC : Estimating Limits from Graphs and Tables

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Example Questions

Example Question #11 : Estimating Limits From Graphs And Tables

Limitplot

$\begin{align*}&\text{Which of the values most likely represents the value of f(x) at}\\&x=\infty\end{align*}$

Possible Answers:

$\frac{19}{15}$

$\infty$

$\text{Nonexistent.}$

Correct answer:

$\text{Nonexistent.}$

Explanation:

$\begin{align*}&\text{Although actually observing a function at an infinite value}\\&\text{of x is impossible, we can often determine via observation if}\\&\text{the function approaches a certain limit. Looking at the values}\\&\text{the function approaches as the absolute value of x increases}\\&\text{gives a clue. Things to look out for are if the function continuously}\\&\text{climbs/decreases, flattens, or has unchecked oscillatory behavior.}\\&\text{If the function continuously climbs/decreases, it likely has}\\&\text{a limit that approaches positive/negative infinity. If it flattens,}\\&\text{the limit is a real number. If it oscillates without control,}\\&\text{the limit does not exist.}\\&\text{The limit of }f(\infty)\text{ is most likely }\text{Nonexistent.}\end{align*}$

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Example Question #12 : Estimating Limits From Graphs And Tables

Limitplot

$\begin{align*}&\text{What is the likely value of}\\&f(-\infty)\\&\text{Based on the graph?}\end{align*}$

Possible Answers:

$\text{Nonexistent.}$

$-\infty$

$\frac{2}{7}$

Correct answer:

$\text{Nonexistent.}$

Explanation:

$\begin{align*}&\text{Although actually observing a function at an infinite value}\\&\text{of x is impossible, we can often determine via observation if}\\&\text{the function approaches a certain limit. Looking at the values}\\&\text{the function approaches as the absolute value of x increases}\\&\text{gives a clue. Things to look out for are if the function continuously}\\&\text{climbs/decreases, flattens, or has unchecked oscillatory behavior.}\\&\text{If the function continuously climbs/decreases, it likely has}\\&\text{a limit that approaches positive/negative infinity. If it flattens,}\\&\text{the limit is a real number. If it oscillates without control,}\\&\text{the limit does not exist.}\\&\text{The limit of }f(-\infty)\text{ is most likely }\text{Nonexistent.}\end{align*}$

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Example Question #13 : Estimating Limits From Graphs And Tables

Limitplot

$\begin{align*}&\text{What is the likely value of}\\&f(-\infty)\\&\text{Based on the graph?}\end{align*}$

Possible Answers:

$-\infty$

$\frac{17}{18}$

$\text{Nonexistent.}$

Correct answer:

Explanation:

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Example Question #14 : Estimating Limits From Graphs And Tables

Limitplot

$\begin{align*}&\text{What is the likely value of}\\&f(-\infty)\\&\text{Based on the graph?}\end{align*}$

Possible Answers:

$\text{Nonexistent.}$

$\frac{1}{4}$

$-\infty$

Correct answer:

$\frac{1}{4}$

Explanation:

$\begin{align*}&\text{Although actually observing a function at an infinite value}\\&\text{of x is impossible, we can often determine via observation if}\\&\text{the function approaches a certain limit. Looking at the values}\\&\text{the function approaches as the absolute value of x increases}\\&\text{gives a clue. Things to look out for are if the function continuously}\\&\text{climbs/decreases, flattens, or has unchecked oscillatory behavior.}\\&\text{If the function continuously climbs/decreases, it likely has}\\&\text{a limit that approaches positive/negative infinity. If it flattens,}\\&\text{the limit is a real number. If it oscillates without control,}\\&\text{the limit does not exist.}\\&\text{The limit of }f(-\infty)\text{ is most likely }\frac{1}{4}\end{align*}$

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Example Question #15 : Estimating Limits From Graphs And Tables

Limitplot

$\begin{align*}&\text{Which of the values most likely represents the value of f(x) at}\\&x=\infty\end{align*}$

Possible Answers:

$-\frac{1331}{512}$

$\infty$

$\text{Nonexistent.}$

Correct answer:

$-\frac{1331}{512}$

Explanation:

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Example Question #16 : Estimating Limits From Graphs And Tables

Limitplot

$\begin{align*}&\text{Based on the graph, decide which of the following functions values likely depicts}\\&f(\infty)\end{align*}$

Possible Answers:

$\infty$

$\frac{17}{12}$

$\text{Nonexistent.}$

Correct answer:

Explanation:

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Example Question #17 : Estimating Limits From Graphs And Tables

Limitplot

$\begin{align*}&\text{Which of the values most likely represents the value of f(x) at}\\&x=\infty\end{align*}$

Possible Answers:

$-\frac{15}{17}$

$\text{Nonexistent.}$

$-\infty$

Correct answer:

$-\infty$

Explanation:

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AP Calculus BC : Estimating Limits from Graphs and Tables

Study concepts, example questions & explanations for AP Calculus BC

All AP Calculus BC Resources

Example Questions

Example Question #11 : Estimating Limits From Graphs And Tables

Example Question #12 : Estimating Limits From Graphs And Tables

Example Question #13 : Estimating Limits From Graphs And Tables

Example Question #14 : Estimating Limits From Graphs And Tables

Example Question #15 : Estimating Limits From Graphs And Tables

Example Question #16 : Estimating Limits From Graphs And Tables

Example Question #17 : Estimating Limits From Graphs And Tables

All AP Calculus BC Resources

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