Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Limits

Study concepts, example questions & explanations for GRE Subject Test: Math

Create An Account

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1681 : Calculus Ii

Evaluate the following limit:

$\lim_{x\rightarrow 3} \frac{3-x}{x^2-9}$

Possible Answers:

$-\frac{1}{6}$

The limit does not exist

$\infty$

$\frac{1}{6}$

Correct answer:

$-\frac{1}{6}$

Explanation:

When we evaluate the limit using normal methods, we arrive at the indeterminate form $\frac{0}{0}$ . When this occurs, to evaluate the limit, we must use L'Hopital's Rule, which states that

$\lim_{x\rightarrow n}\frac{ f(x)}{g(x)}=\lim_{x\rightarrow n} \frac{f'(x)}{g'(x)}$

So, we must find the derivative of the top and bottom functions:

f'(x)=-1, g'(x)=2x

The derivatives were found using the following rule:

$\frac{\mathrm{d} }{\mathrm{d} x} x^n=nx^{n-1}$

Now, rewrite the limit and evaluate it:

$\lim_{x\rightarrow 3}-\frac{1}{2x}=-\frac{1}{6}$

Report an Error

Example Question #23 : L'hospital's Rule

Evaluate the following limit:

$\lim_{x\rightarrow 2}\frac{x^2-4}{\sin(2-x)}$

Possible Answers:

$\infty$

Correct answer:

Explanation:

When we evaluate the limit using normal methods, we get the indeterminate form $\frac{0}{0}$ . When this happens, we must use L'Hopital's Rule, which states that $\lim_{x\rightarrow n}\frac{f(x)}{g(x)}=\lim_{x\rightarrow n}\frac{f'(x)}{g'(x)}$

Now, we must find the derivatives of the numerator and denominator:

$f'(x)=2x, g'(x)=-\cos(x-4)$

The derivatives were found using the following rules:

$\frac{\mathrm{d} }{\mathrm{d} x} x^n=nx^{n-1}$ , $\frac{\mathrm{d} }{\mathrm{d} x} f(g(x))=f'(g(x))\cdot g'(x)$ , $\frac{\mathrm{d} }{\mathrm{d} x} \sin(x)=\cos(x)$

Next, rewrite the limit and evaluate it:

$\lim_{x\rightarrow 2}\frac{2x}{-\cos(2-x)}=-4$

Report an Error

Example Question #24 : L'hospital's Rule

Use l'Hopital's rule to find the limit:

$\lim_{x \to 1} \frac{x^2-3x+2}{x-1}$

Possible Answers:

$\infty$

Correct answer:

Explanation:

The first thing we always have to do is to check that l'Hopital's rule is actually applicable when we want to use it.

$\frac{1^2-3\cdot1+2}{1-1} = \frac{0}{0}$

So it is applicable here.

We take the derivative of the top and bottom, and get

$\lim_{x \to 1} \frac{x^2-3x+2}{x-1} = \lim_{x \to 1} \frac{2x-3}{1}$

and now we can safely plug in x=1 and get that the limit equals

$2\cdot 1 -3 = -1$ .

Report an Error

View Tutors

Chase
Certified Tutor

Western Governors University, Bachelor of Science, Mathematics.

View Tutors

Mohammed
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Electrical Engineering. University of Maryland-College Park, Master...

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Atlanta, Spanish Tutors in Houston, LSAT Tutors in New York City, ACT Tutors in Denver, ISEE Tutors in San Diego, French Tutors in Miami, GRE Tutors in Chicago, Chemistry Tutors in Chicago, English Tutors in Chicago, ISEE Tutors in Chicago

Popular Courses & Classes

GMAT Courses & Classes in New York City, LSAT Courses & Classes in Chicago, GRE Courses & Classes in Boston, ACT Courses & Classes in Chicago, LSAT Courses & Classes in Boston, GMAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Phoenix, SSAT Courses & Classes in Phoenix, LSAT Courses & Classes in New York City

Popular Test Prep

LSAT Test Prep in San Diego, GRE Test Prep in Washington DC, SSAT Test Prep in Los Angeles, MCAT Test Prep in Boston, LSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Denver, LSAT Test Prep in New York City, SAT Test Prep in Washington DC, SSAT Test Prep in Chicago, MCAT Test Prep in Washington DC

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

GRE Subject Test: Math : Limits

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #1681 : Calculus Ii

Example Question #23 : L'hospital's Rule

Example Question #24 : L'hospital's Rule

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: