We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Calculus II

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 #31 : Parametric, Polar, And Vector

Convert the following function from parametric to rectangular coordinates:

x=t^2+4 , y=t+2

Possible Answers:

$y=2-\sqrt{x-4}$

$y=2+\sqrt{x-4}$

$y=2\pm \sqrt{x+4}$

$y=2\pm \sqrt{x-4}$

Correct answer:

$y=2\pm \sqrt{x-4}$

Explanation:

To convert to rectangular coordinates, eliminate the parameter by setting one of the functions equal to t:

$t=\pm \sqrt{x-4}$

To finish, substitute this into the equation for y:

$y=2\pm \sqrt{x-4}$

Report an Error

Example Question #39 : Parametric, Polar, And Vector

Given x=4t+14 and y=5t-2 , what is in terms (rectangular form)?

Possible Answers:

$y=\frac{5}{4}(x-14)-2$

$y=\frac{5}{4}(x+14)-2$

$y=\frac{5}{4}(x+14)+2$

None of the above

$y=\frac{5}{4}(x-14)+2$

Correct answer:

$y=\frac{5}{4}(x-14)-2$

Explanation:

Given x=4t+14 and y=5t-2 , let's solve both equations for :

$x=4t+14\rightarrow t=\frac{x-14}{4}$

$y=5t-2\rightarrow t=\frac{y+2}{5}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y+2}{5}=\frac{x-14}{4}$

$y+2=5(\frac{x-14}{4})$

$y=\frac{5}{4}(x-14)-2$

Report an Error

Example Question #40 : Parametric, Polar, And Vector

Given x=t-5 and y=2t+11 , what is in terms (rectangular form)?

Possible Answers:

y=2x-21

None of the above

y=2x+1

y=2x-1

y=2x+21

Correct answer:

y=2x+21

Explanation:

Given x=t-5 and y=2t+11 , let's solve both equations for :

$x=t-5\rightarrow t=x+5$

$y=2t+11\rightarrow t=\frac{y-11}{2}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-11}{2}=x+5$

y-11=2(x+5)

y=2(x+5)+11

y=2x+10+11

y=2x+21

Report an Error

Example Question #41 : Parametric, Polar, And Vector

Given x=3t+7 and y=7t+3 , what is in terms (rectangular form)?

Possible Answers:

$y=\frac{7}{3}(x+7)+3$

$y=\frac{3}{7}(x-7)+3$

$y=\frac{7}{3}(x-7)+3$

$y=\frac{3}{7}(x+7)+3$

$y=\frac{7}{3}(x-7)-3$

Correct answer:

$y=\frac{7}{3}(x-7)+3$

Explanation:

Given x=3t+7 and y=7t+3 , let's solve both equations for :

$x=3t+7\rightarrow t=\frac{x-7}{3}$

$y=7t+3\rightarrow t=\frac{y-3}{7}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-3}{7}=\frac{x-7}{3}$

$y-3=7(\frac{x-7}{3})$

$y=\frac{7}{3}(x-7)+3$

Report an Error

Example Question #42 : Parametric, Polar, And Vector

Given x=7t+5 and y=11t+2 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{11}{7}(x+5)+2$

$y=\frac{11}{7}(x+5)-2$

$y=\frac{11}{7}(x-5)+2$

None of the above

$y=\frac{11}{7}(x-5)-2$

Correct answer:

$y=\frac{11}{7}(x-5)+2$

Explanation:

Given x=7t+5 and y=11t+2 , let's solve both equations for :

$x=7t+5\rightarrow t=\frac{x-5}{7}$

$y=11t+2\rightarrow t=\frac{y-2}{11}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-2}{11}=\frac{x-5}{7}$

$y-2=11(\frac{x-5}{7})$

$y=\frac{11}{7}(x-5)+2$

Report an Error

Example Question #43 : Parametric

Given x=-6t+11 and y=2t-10 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{x-11}{3}+10$

$y=\frac{x-11}{3}-10$

$y=-\frac{x-11}{3}+10$

None of the above

$y=-\frac{x-11}{3}-10$

Correct answer:

$y=-\frac{x-11}{3}-10$

Explanation:

Given x=-6t+11 and y=2t-10 let's solve both equations for :

$x=-6t+11\rightarrow t=-\frac{x-11}{6}$

$y=2t-10\rightarrow t=\frac{y+10}{2}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y+10}{2}=-\frac{x-11}{6}$

$y+10=-2(\frac{x-11}{6})$

$y=-\frac{x-11}{3}-10$

Report an Error

Example Question #41 : Parametric, Polar, And Vector

Convert the following equation from parametric to rectangular coordinates:

x=2t^2, y=10t

Possible Answers:

$y=-10\sqrt{\frac{x}{2}}$

y=5x

$y=\pm10\sqrt{\frac{x}{2}}$

$y=10\sqrt{\frac{x}{2}}$

Correct answer:

$y=\pm10\sqrt{\frac{x}{2}}$

Explanation:

To convert the equation from parametric form to rectangular form, we must eliminate the parameter. To do this, we can solve for t with respect to x:

$t=\pm \sqrt{\frac{x}{2}}$

The plus or minus is important to remember because a square root was taken.

Now, simply plug this into the equation for y:

$y=\pm10\sqrt{\frac{x}{2}}$

Report an Error

Example Question #45 : Parametric

Convert the following to rectangular form from parametric form:

x=2t^3+5 , y=t

Possible Answers:

y=x

$y=\frac{x-5}{2}$

$y=\sqrt[3]{\left(\frac{x-5}{2}\right)}$

$y=\left(\frac{x-5}{2}\right)^{\frac{3}{2}}$

Correct answer:

$y=\sqrt[3]{\left(\frac{x-5}{2}\right)}$

Explanation:

To convert a parametric equation into a rectangular equation, we must eliminate the parameter. We were already given an equation where t was in terms of just a variable:

t=y

Next, substitute this into the equation for x which contains t:

x=2(y^3)+5

Finally, rearrage and solve for y:

$y=\sqrt[3]{\left(\frac{x-5}{2}\right)}$

Report an Error

Example Question #42 : Parametric, Polar, And Vector

Convert the following equation into rectanglar form:

$x=\cos(t), y=cos^2 (t)+3$

Possible Answers:

y=-x^2+3

y=x^2+3

$y=\arccos(x)+3$

$y=\cos(x)+3$

Correct answer:

y=x^2+3

Explanation:

To convert the given parametric equation into rectangualr coordinates, we must eliminate the parameter by solving for t:

$t=\arccos (x)$

Now replace t with the new term in the equation for y:

$y= (\cos(\textup{arccos}(x)^2)+3=x^2+3$

Report an Error

Example Question #43 : Parametric, Polar, And Vector

Convert the following equation from parametric to rectangular form:

$x=e^t, y=2\sin(t)$

Possible Answers:

$y=-2\sin(\ln(x))$

$y=2\sin(\ln(x))$

y=x

$y=2\sin(e^t)$

Correct answer:

$y=2\sin(\ln(x))$

Explanation:

To convert from parametric to rectangular form, eliminate the parameter (t) from one of the equations:

$t=\ln(x)$

Now plug this into the equation for y to get our final answer:

$y=2\sin(\ln(x))$

Report an Error

View Calculus 2 Tutors

Dalton
Certified Tutor

University of Massachusetts Amherst, Doctor of Philosophy, Mathematics.

View Calculus 2 Tutors

Gregory
Certified Tutor

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

View Calculus 2 Tutors

Adam
Certified Tutor

Arizona State University, Bachelor of Science, Mathematics.

All Calculus 2 Resources

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

Popular Subjects

French Tutors in Atlanta, ISEE Tutors in Washington DC, Algebra Tutors in San Diego, Math Tutors in San Francisco-Bay Area, Biology Tutors in Washington DC, Spanish Tutors in Boston, LSAT Tutors in San Diego, ACT Tutors in Miami, Spanish Tutors in New York City, Spanish Tutors in Chicago

Popular Courses & Classes

ISEE Courses & Classes in Boston, ACT Courses & Classes in Denver, GRE Courses & Classes in New York City, GMAT Courses & Classes in Miami, GMAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Houston, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Washington DC, LSAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in San Diego

Popular Test Prep

GRE Test Prep in Phoenix, SSAT Test Prep in Philadelphia, LSAT Test Prep in Los Angeles, ISEE Test Prep in Phoenix, LSAT Test Prep in New York City, ISEE Test Prep in Washington DC, GMAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Miami, ACT Test Prep in Houston, MCAT 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 : Calculus II

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #31 : Parametric, Polar, And Vector

Example Question #39 : Parametric, Polar, And Vector

Example Question #40 : Parametric, Polar, And Vector

Example Question #41 : Parametric, Polar, And Vector

Example Question #42 : Parametric, Polar, And Vector

Example Question #43 : Parametric

Example Question #41 : Parametric, Polar, And Vector

Example Question #45 : Parametric

Example Question #42 : Parametric, Polar, And Vector

Example Question #43 : Parametric, Polar, And Vector

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: