Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : 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 #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

Example Question #271 : Finding Limits And One Sided Limits

Evaluate the limit:

$\lim_{x \to 6}5x+6$

Possible Answers:

$-\infty$

$\infty$

DNE

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:

$\lim_{x \to 6}5x+6=5*6+6=30+6=36$

Report an Error

Example Question #272 : Finding Limits And One Sided Limits

Evaluate the limit:

$\lim_{x \to 10}x^2-2x+80$

Possible Answers:

$-\infty$

160

DNE

$\infty$

Correct answer:

160

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:

$\lim_{x \to 10}x^2-2x+80=10^2-2*10+80=100-20+80=80+80=160$

Report an Error

Example Question #273 : Finding Limits And One Sided Limits

Evaluate the limit:

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

Possible Answers:

$\infty$

DNE

$-\infty$

Correct answer:

Explanation:

The limiting situation in this equation would be the denominator. Plug the value that x is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will not equal zero when x=h; so we proceed to insert the value of x into the entire equation.

$\lim_{x \to h}\frac{x^2-h^2}{x+h}=\frac{h^2-h^2}{h+h}=\frac{0}{2h}=0$

Report an Error

Example Question #274 : Finding Limits And One Sided Limits

Evaluate the limit:

$\lim_{x \to 5}\frac{x^2+2x+10}{x+5}$

Possible Answers:

$\infty$

DNE

4.5

$-\infty$

Correct answer:

4.5

Explanation:

The limiting situation in this equation would be the denominator. Plug the value that x is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will not equal zero when x=5; so we proceed to insert the value of x into the entire equation.

$\lim_{x \to 5}\frac{x^2+2x+10}{x+5}=\frac{5^2+2*5+10}{5+5}=\frac{25+10+10}{10}=\frac{45}{10}=4.5$

Report an Error

Example Question #274 : Finding Limits And One Sided Limits

Evaluate the limit:

$\lim_{x \to 5}\sqrt{x^2-2x+1}$

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:

$\lim_{x \to 5}\sqrt{x^2-2x+1}= \lim_{x \to 5}\sqrt{(x-1)^2}=\lim_{x \to 5}x-1=5-1=4$

Report an Error

Example Question #275 : Finding Limits And One Sided Limits

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

Possible Answers:

$-\infty$

$\sqrt{2}$

$\infty$

DNE

Correct answer:

$\sqrt{2}$

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:

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

Report an Error

Example Question #276 : Finding Limits And One Sided Limits

Evaluate the limit:

$\lim_{x \to 1}(x+2)^3$

Possible Answers:

$\infty$

$-\infty$

DNE

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:

$\lim_{x \to 1}(x+2)^3=(1+2)^3=3^3=27$

Report an Error

View Calculus 2 Tutors

Jack
Certified Tutor

University of Washington-Seattle Campus, Bachelor in Arts, Mathematics. Western Washington University, Master of Science, Mat...

View Calculus 2 Tutors

Sharif
Certified Tutor

University of South Florida-Main Campus, Bachelor of Science, Cellular and Molecular Biology.

View Calculus 2 Tutors

Conrad
Certified Tutor

Vanderbilt University, Bachelor of Engineering, Engineering Science.

All Calculus 2 Resources

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

Popular Subjects

Math Tutors in Houston, ACT Tutors in San Francisco-Bay Area, Statistics Tutors in Washington DC, ISEE Tutors in San Francisco-Bay Area, SAT Tutors in Philadelphia, ACT Tutors in Los Angeles, SAT Tutors in Boston, Math Tutors in Chicago, English Tutors in Seattle, Physics Tutors in Phoenix

Popular Courses & Classes

GMAT Courses & Classes in Miami, SSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Boston, SAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in New York City, SSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Washington DC

Popular Test Prep

GRE Test Prep in Chicago, GMAT Test Prep in Denver, ISEE Test Prep in Houston, ISEE Test Prep in Dallas Fort Worth, LSAT Test Prep in Washington DC, GMAT Test Prep in New York City, SSAT Test Prep in Atlanta, LSAT Test Prep in Denver, GMAT Test Prep in Dallas Fort Worth, GMAT Test Prep in San Diego

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 : Limits

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

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

Example Question #271 : Finding Limits And One Sided Limits

Example Question #272 : Finding Limits And One Sided Limits

Example Question #273 : Finding Limits And One Sided Limits

Example Question #274 : Finding Limits And One Sided Limits

Example Question #274 : Finding Limits And One Sided Limits

Example Question #275 : Finding Limits And One Sided Limits

Example Question #276 : 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: