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Calculus 2 : Finding Limits and One-Sided Limits

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Example Questions

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Example Question #61 : Limits

Screen shot 2015 07 01 at 11.01.45 am

Given the above graph of a function , what is $\lim_{x\rightarrow \infty }f(x)$ ?

Possible Answers:

$-\infty$

$\infty$

Correct answer:

Explanation:

Examining the graph, we can observe that, as approaches $\infty$ , $\lim_{x\rightarrow \infty }f(x)=7$ .

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Example Question #62 : Limits

Screen shot 2015 07 01 at 11.14.04 am

Given the above graph of a function , what is $\lim_{x\rightarrow 0^{-} }f(x)$ ?

Possible Answers:

$-\infty$

Does Not Exist

$\infty$

Correct answer:

$\infty$

Explanation:

Examining the graph, we can observe that, as approaches from the left, $\lim_{x\rightarrow 0^{-} }f(x)=\infty$ .

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Example Question #61 : Limits

Screen shot 2015 07 01 at 11.23.33 am

Given the above graph of a function , what is $\lim_{x\rightarrow 0 }f(x)$ ?

Possible Answers:

$\infty$

None of the above

$-\infty$

Does Not Exist

Correct answer:

Does Not Exist

Explanation:

Examining the graph, we can observe that $\lim_{x\rightarrow 0 }f(x)$ approaches two different limits as approaches ( $\infty$ and $-\infty$ ) , depending entirely on which side approaches from. Therefore, a singular limit does not exist.

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Example Question #64 : Limits

Screen shot 2015 07 03 at 12.33.12 pm

Given the above graph of f(x) , what is $\lim_{x\rightarrow 0}f(x)$ ?

Possible Answers:

$\infty$

$-\infty$

Correct answer:

Explanation:

By examining the above graph of f(x) , we can observe that as approaches from either side, $\lim_{x\rightarrow 0}f(x)=0$ .

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Example Question #65 : Limits

Screen shot 2015 07 03 at 12.42.38 pm

Given the above graph of f(x) , what is $\lim_{x\rightarrow 0}f(x)$ ?

Possible Answers:

Does Not Exist

$\infty$

$-\infty$

Correct answer:

Does Not Exist

Explanation:

By examining the above graph of f(x) , we can observe that $\lim_{x\rightarrow 0}f(x)$ produces two different values as approaches from either side $\infty$ and $-\infty$ . Thus, a singular limit does not exist for this function.

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Example Question #21 : Finding Limits And One Sided Limits

Screen shot 2015 07 03 at 4.06.06 pm

Given the above graph of f(x) , what is $\lim_{x\rightarrow 0}f(x)$ ?

Possible Answers:

$\infty$

$-\infty$

Correct answer:

Explanation:

Examining the graph of f(x) , we can see that as approaches from either side, $\lim_{x\rightarrow 0}f(x)=0$ .

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Example Question #67 : Limits

Screen shot 2015 07 03 at 4.14.41 pm

Given the above graph of f(x) , what is $\lim_{x\rightarrow 0^{-}}f(x)$ ?

Possible Answers:

$-\infty$

$\infty$

Correct answer:

$-\infty$

Explanation:

Examining the graph of f(x) , we can see that as approaches from the left side, $\lim_{x\rightarrow 0^{-}}f(x)=-\infty$ .

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Example Question #71 : Limits

Screen shot 2015 07 03 at 4.27.08 pm

Given the above graph of f(x) , what is $\lim_{x\rightarrow 0}f(x)$ ?

Possible Answers:

$\infty$

$-\infty$

Correct answer:

$\infty$

Explanation:

Examining the graph of f(x) , we can see that as approaches from either side, $\lim_{x\rightarrow 0}f(x)=\infty$ .

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Example Question #71 : Limits

Screen shot 2015 07 07 at 4.02.20 pm

Given the graph of f(x) above, what is $\lim_{x\rightarrow 0^{-}}f(x)$ ?

Possible Answers:

$\infty$

$-\infty$

Correct answer:

$-\infty$

Explanation:

Examining the graph above, we can determine that $\lim_{x\rightarrow 0^{-}}f(x)=-\infty$ as approaches from the left.

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Example Question #1 : Limits

For the piecewise function:

$y=\left\{\begin{matrix} 1 \textup{, for }x> 0\\ 0 \textup{, for }x< 0\end{matrix}\right.$ , find $\lim_{x\to 0^+}$ .

Possible Answers:

$\frac{1}{2}$

Any real number.

Does not exist.

Correct answer:

Explanation:

The limit $\lim_{x\to 0^+}$ indicates that we are trying to find the value of the limit as approaches to zero from the right side of the graph.

From right to left approaching x=0 , the limit approaches to 1 even though the value at x=0 of the piecewise function does not exist.

The answer is .

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Calculus 2 : Finding Limits and One-Sided Limits

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #61 : Limits

Example Question #62 : Limits

Example Question #61 : Limits

Example Question #64 : Limits

Example Question #65 : Limits

Example Question #21 : Finding Limits And One Sided Limits

Example Question #67 : Limits

Example Question #71 : Limits

Example Question #71 : Limits

Example Question #1 : Limits

All Calculus 2 Resources

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