Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Finding Limits and One-Sided Limits

Study concepts, example questions & explanations for Calculus 2

Create An Account

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #301 : Calculus Ii

What is the $\lim_{x \rightarrow 6^+} y$ , given the following graph of ,

$y=\frac{x^2+4}{x-6}$

Possible Answers:

Does not exist

$\infty$

$-\infty$

Correct answer:

$\infty$

Explanation:

As shown by the graph, the limit as goes to from the right is infinity.

To make sure that the right limit is at , we can plug the number into the denominator of the function and see if the denominator equals .

x-6 = 6-6 = 0

The denominator is equal to , so we can say that limit is infinity.

Report an Error

Example Question #302 : Calculus Ii

What is the $\lim_{x \rightarrow 3^+} y$ , given the following graph of ,

$y=\frac{x+4}{x^3-27}$

Possible Answers:

$-\infty$

Does not exist

$\infty$

Correct answer:

$\infty$

Explanation:

As shown by the graph, the limit as goes to from the right is infinity.

To make sure that the right limit is , we can plug the number into the denominator of the function and see if the denominator equals .

x^3-27 = 3^3 - 27 = 27-27 = 0

The denominator is equal to , so this limit will go to infinity as goes to from the right.

Report an Error

Example Question #301 : Calculus Ii

Let f(x) be the piecewise function denoted below

$f(x)=\left\{\begin{matrix} 3& x<2\\ x^2& x\geq 2 \end{matrix}\right.$

Evaluate the limit

$\lim_{x\rightarrow 2^+}f(x)$

Possible Answers:

DNE

Correct answer:

Explanation:

The limit

$\lim_{x\rightarrow a^+}f(x)$

denotes the limit of the function f(x) as approaches from the right.

For $\lim_{x\rightarrow 2^+}f(x)$

We can evaluate $f(2.1), \,f(2.01)$ , and f(2.001) to find the limit.

Because $2.1,\, 2.01,\, 2.001 \geq 2$

f(2.1)=2.1^2=4.41

f(2.01)=2.01^2=4.0401

f(2.001)=2.001^2=4.004001

From this pattern we find the limit to be

$\lim_{x\rightarrow 2^+}f(x) =4$

Report an Error

Example Question #301 : Limits

Let f(x) be the piecewise function denoted below

$f(x)=\left\{\begin{matrix} 4& x<0\\ e^x& x\geq 0 \end{matrix}\right.$

Evaluate the limit

$\lim_{x\rightarrow 0^-}f(x)$

Possible Answers:

DNE

Correct answer:

Explanation:

The limit

$\lim_{x\rightarrow a^-}f(x)$

denotes the limit of the function f(x) as approaches from the left.

For $\lim_{x\rightarrow 0^-}f(x)$

We can evaluate $f(-0.1), \,f(-0.01)$ , and f(-0.001) to find the limit.

Because $-0.1,\, -0.01,\, -0.001 < 0$

f(-0.1)=4

f(-0.01)=4

f(-0.001)=4

From this pattern we find the limit to be

$\lim_{x\rightarrow 0^-}f(x) =4$

Report an Error

Example Question #305 : Calculus Ii

Let f(x) be the piecewise function denoted below

$f(x)=\left\{\begin{matrix} 1& x<0\\ e^x& x\geq 0 \end{matrix}\right.$

Evaluate the limit if it exists

$\lim_{x\rightarrow 0}f(x)$

Possible Answers:

DNE

$\infty$

Correct answer:

Explanation:

The limit

$\lim_{x\rightarrow 0}f(x)$

exists if

$\lim_{x\rightarrow 0^-}f(x)=\lim_{x\rightarrow 0^+}f(x)$

Because

$\lim_{x\rightarrow 0^-}f(x)=1$

and

$\lim_{x\rightarrow 0^+}f(x)=e^0=1$

We find that $\lim_{x\rightarrow 0^-}f(x)=\lim_{x\rightarrow 0^+}f(x)$

and the limit exists.

As such

$\lim_{x\rightarrow 0}f(x)=1$

Report an Error

Example Question #301 : Limits

Evaluate the following limit:

$\lim_{x\rightarrow \infty} \frac{x^2}{x+e^x}$

Possible Answers:

$\frac{1}{2}$

$-\infty$

$\infty$

Correct answer:

Explanation:

While the numerator of the function is a larger degree polynomial than the denominator, the exponential function in the denominator grows faster than the polynomial. Therefore, as the limit approaches infinity, the denominator becomes far larger than the numerator, making the fraction go to .

Report an Error

Example Question #302 : Limits

Evaluate the limit:

$\lim_{x \to 0}x^2+2x+4$

Possible Answers:

DNE

$-\infty$

$\infty$

Correct answer:

Explanation:

There is no limiting situation in this equation (like a denominator) so we can just plug in the value that n approaches into the limit and solve:

$\lim_{x \to 0}x^2+2x+4=0^2+2*0+4=4$

Report an Error

Example Question #261 : Finding Limits And One Sided Limits

Evaluate the limit:

$\lim_{x \to h}x^3-2x^2+3x-10$

Possible Answers:

$\infty$

DNE

$-\infty$

h^3-2h^2+3h-10

Correct answer:

h^3-2h^2+3h-10

Explanation:

There is no limiting situation in this equation (like a denominator) so we can just plug in the value that n approaches into the limit and solve:

$\lim_{x \to h}x^3-2x^2+3x-10=h^3-2h^2+3h-10$

Report an Error

Example Question #262 : Finding Limits And One Sided Limits

Evaluate the limit:

$\lim_{x \to 4}x^2-8x+16$

Possible Answers:

DNE

$\infty$

$-\infty$

Correct answer:

Explanation:

There is no limiting situation in this equation (like a denominator) so we can just plug in the value that n approaches into the limit and solve:

$\lim_{x \to 4}x^2-8x+16=4^2-8*4+16=16-32+16=32-32=0$

Report an Error

Example Question #263 : Finding Limits And One Sided Limits

Evaluate the limit:

$\lim_{x \to ab}x-ab+2a^2b^2$

Possible Answers:

DNE

2a^2b^2

$\infty$

$-\infty$

Correct answer:

2a^2b^2

Explanation:

There is no limiting situation in this equation (like a denominator) so we can just plug in the value that n approaches into the limit and solve:

$\lim_{x \to ab}x-ab+2a^2b^2=ab-ab+2a^2b^2=2a^2b^2$

Report an Error

View Calculus 2 Tutors

Eric
Certified Tutor

University of Wisconsin-Madison, Bachelor of Science, Applied Physics.

View Calculus 2 Tutors

Samuel
Certified Tutor

Millikin University, Bachelor of Science, Mathematics.

View Calculus 2 Tutors

Filiberto
Certified Tutor

University of Arizona, Bachelor of Science, Electrical Engineering.

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in Washington DC, Statistics Tutors in Houston, Physics Tutors in San Francisco-Bay Area, English Tutors in Philadelphia, LSAT Tutors in Dallas Fort Worth, Statistics Tutors in Washington DC, English Tutors in Atlanta, French Tutors in Phoenix, Spanish Tutors in Miami, Computer Science Tutors in Seattle

Popular Courses & Classes

SSAT Courses & Classes in Los Angeles, SAT Courses & Classes in Philadelphia, ACT Courses & Classes in Chicago, ACT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Phoenix, SSAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in New York City, Spanish Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Los Angeles, ISEE Courses & Classes in Atlanta

Popular Test Prep

SSAT Test Prep in Houston, ISEE Test Prep in Dallas Fort Worth, ISEE Test Prep in Denver, ISEE Test Prep in San Francisco-Bay Area, GMAT Test Prep in New York City, SAT Test Prep in Miami, SSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Phoenix, ACT Test Prep in Chicago, ACT Test Prep in Atlanta

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Calculus 2 : Finding Limits and One-Sided Limits

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #301 : Calculus Ii

Example Question #302 : Calculus Ii

Example Question #301 : Calculus Ii

Example Question #301 : Limits

Example Question #305 : Calculus Ii

Example Question #301 : Limits

Example Question #302 : Limits

Example Question #261 : Finding Limits And One Sided Limits

Example Question #262 : Finding Limits And One Sided Limits

Example Question #263 : Finding Limits And One Sided Limits

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: