Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Parametric

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 #3 : Derivatives Of Parametrics

Solve for $\frac{dy}{dx}$ if x=9t+1 and y=4t+10 .

Possible Answers:

None of the above

$\frac{4}{9}$

$-\frac{9}{4}$

$-\frac{4}{9}$

$\frac{9}{4}$

Correct answer:

$\frac{4}{9}$

Explanation:

We can determine that $\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$ since the terms will cancel out in the division process.

Since x=9t+1 and y=4t+10 , we can use the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ to derive

$\frac{dx}{dt}=(1)9t^{1-1}+(0)1=9$ and $\frac{dy}{dt}=(1)4t^{1-1}+(0)10=4$ .

Thus:

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{4}{9}}$ .

Report an Error

Example Question #121 : Parametric, Polar, And Vector

What is $\frac{dy}{dx}$ when x=2t+13 and y=4t+17 ?

Possible Answers:

None of the above

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

Explanation:

We can first recognize that

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

since cancels out when we divide.

Then, given x=2t+13 and y=4t+17 and using the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ ,

we can determine that

$\frac{dy}{dt}=(1)4t^{1-1}+(0)17=4$ and $\frac{dx}{dt}=(1)2t^{1-1}+(0)13=2$ .

Therefore,

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{4}{2}=2$ .

Report an Error

Example Question #12 : Derivatives Of Parametrics

What is $\frac{dy}{dx}$ when x=-t+12 and $y=\frac{8}{t}$ ?

Possible Answers:

None of the above

$-\frac{t^{2}}{8}$

$\frac{8}{t^{2}}$

$-\frac{8}{t^{2}}$

$\frac{t^{2}}{8}$

Correct answer:

$\frac{8}{t^{2}}$

Explanation:

We can first recognize that

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

since cancels out when we divide.

Then, given x=-t+12 and $y=\frac{8}{t}$ or $y=8t^{-1}$ and using the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ ,

we can determine that

$\frac{dy}{dt}=(-1)8t^{-1-1}=-\frac{8}{t^{2}}$ and $\frac{dx}{dt}=(1)(-1)t^{1-1}+(0)12=-1$ .

Therefore,

$\frac{dy}{dx}=\frac{-\frac{8}{t^{2}}}{-1}=\frac{8}{t^{2}}$ .

Report an Error

Example Question #121 : Parametric

What is $\frac{dy}{dx}$ when x=-6t+10 and y=7t-2 ?

Possible Answers:

$\frac{6}{7}$

$-\frac{7}{6}$

None of the above

$-\frac{6}{7}$

$\frac{7}{6}$

Correct answer:

$-\frac{7}{6}$

Explanation:

We can first recognize that

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

since cancels out when we divide.

Then, given x=-6t+10 and y=7t-2 and using the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ ,

we can determine that

$\frac{dy}{dt}=(1)7t^{1-1}-(0)2=7$ and $\frac{dx}{dt}=(1)(-6)t^{1-1}+(0)10=-6$ .

Therefore,

$\frac{dy}{dx}=\frac{7}{-6}=-\frac{7}{6}$ ..

Report an Error

Example Question #122 : Parametric, Polar, And Vector

Find the derivative of the curve defined by the parametric equations.

x(t)=3sin(t)

y(t)=t^2+4t

Possible Answers:

$\frac{dy}{dx}=-\frac{2t+4}{3sin(t)cos(t)}$

$\frac{dy}{dx}=3cos(t)+2t+4$

$\frac{dy}{dx}=\frac{6t^2cos(t)+10tcos(t)-4cos(t)}{9cos^2(t)}$

$\frac{dy}{dx}=\frac{2t+4}{3cos(t)}$

Correct answer:

$\frac{dy}{dx}=\frac{2t+4}{3cos(t)}$

Explanation:

The first derivative of a parametrically defined curve is found by computing

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$ .

We need to find the derivatives of y(t) and x(t) separately, and then find the quotient of the derivatives.

You will need to know that

$\frac{d}{dt}sin(t)=cos(t)$ and that $\frac{d}{dt}t^n=nt^{n-1}$ .

$x'(t)=\frac{dx}{dt}=3cos(t)$

$y'(t)=\frac{dy}{dt}=2t+4$

Thus,

$\frac{dy}{dx}=\frac{2t+4}{3cos(t)}$

Report an Error

Example Question #123 : Parametric, Polar, And Vector

Find the derivative of the following parametric function:

x=t^3+2t^2+4t, y=2t

Possible Answers:

$\frac{2}{3t^2+4t+4}$

$\frac{3t^2+4t+4}{2}$

3t^2+4t+4

Correct answer:

$\frac{2}{3t^2+4t+4}$

Explanation:

The derivative of a parametric equation is given by the following equation:

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

The derivative of the equation for is

$\frac{dy}{dt}=2$

and the derivative of the equation for is

$\frac{dx}{dt}=3t^2+4t+4$

The derivatives were found using the following rule:

$\frac{d}{dx}(x^n)=nx^{n-1}$

Report an Error

Example Question #124 : Parametric, Polar, And Vector

Find the derivative of the following parametric function:

x=3t+5 , $y=te^t+\cos^2(t)$

Possible Answers:

$\frac{e^t-2\cos(t)\sin(t)}{3}$

$\frac{e^t+te^t+2\cos(t)\sin(t)}{3}$

$\frac{e^t+te^t-2\cos(t)\sin(t)}{3}$

$\frac{2\cos(t)\sin(t)}{3}$

Correct answer:

$\frac{e^t+te^t-2\cos(t)\sin(t)}{3}$

Explanation:

The derivative of a parametric function is given by

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

So, we must find the derivative of the functions with respect to t:

$y'=e^t+te^t-2\cos(t)\sin(t)$ , x'=3

The derivatives were found using the following rules:

$\frac{d}{dx}(x^n)=nx^{n-1}$ , $\frac{d}{dx}(e^x)=e^x$ $\frac{d}{dx}\cos(t)=-\sin(t)$ , $\frac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x)$

Simply divide the derivatives to get your answer.

Report an Error

Example Question #121 : Parametric

What is $\frac{dy}{dx}$

if x=10t-3 and y=2t+9 ?

Possible Answers:

$-\frac{1}{5}$

None of the above

$\frac{1}{5}$

Correct answer:

$\frac{1}{5}$

Explanation:

We can first recognize that

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

since cancels out when we divide.

Then, given x=10t-3 and y=2t+9 and using the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ , we can determine that

$\frac{dx}{dt}=(1)10t^{1-1}-(0)3=10$ and

$\frac{dy}{dt}=(1)2t^{1-1}+(0)9=2$ .

Therefore,

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{2}{10}=\frac{1}{5}$ .

Report an Error

Example Question #125 : Parametric, Polar, And Vector

What is $\frac{dy}{dx}$

if x=3t+2 and y=9t-5 ?

Possible Answers:

$\frac{1}{3}$

None of the above

$-\frac{1}{3}$

Correct answer:

Explanation:

We can first recognize that

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

since cancels out when we divide.

Then, given x=3t+2 and y=9t-5 and using the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ , we can determine that

$\frac{dx}{dt}=(1)3t^{1-1}+(0)2=3$ and

$\frac{dy}{dt}=(1)9t^{1-1}-(0)5=9$ .

Therefore,

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{9}{3}=3$ .

Report an Error

Example Question #126 : Parametric, Polar, And Vector

What is $\frac{dy}{dx}$

if x=5t-1 and y=t+5 ?

Possible Answers:

$-\frac{1}{5}$

None of the above

$\frac{1}{5}$

Correct answer:

$\frac{1}{5}$

Explanation:

We can first recognize that

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

since cancels out when we divide.

Then, given x=5t-1 and y=t+5 and using the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ , we can determine that

$\frac{dx}{dt}=(1)5t^{1-1}-(0)1=5$ and

$\frac{dy}{dt}=(1)t^{1-1}+(0)5=1$ .

Therefore,

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{1}{5}$ .

Report an Error

View Calculus 2 Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Calculus 2 Tutors

Filiberto
Certified Tutor

University of Arizona, Bachelor of Science, Electrical Engineering.

View Calculus 2 Tutors

Chelsea
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Physics. The University of Texas at Dallas, Master of Science, Bioinf...

All Calculus 2 Resources

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

Popular Subjects

GRE Tutors in New York City, MCAT Tutors in Washington DC, Math Tutors in Houston, Chemistry Tutors in Denver, Biology Tutors in Atlanta, Biology Tutors in San Diego, MCAT Tutors in Houston, English Tutors in Seattle, English Tutors in Boston, SAT Tutors in Los Angeles

Popular Courses & Classes

SAT Courses & Classes in San Diego, MCAT Courses & Classes in Boston, SAT Courses & Classes in Phoenix, ISEE Courses & Classes in Phoenix, ACT Courses & Classes in Phoenix, GRE Courses & Classes in Washington DC, SSAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Washington DC, ACT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Chicago

Popular Test Prep

SSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Seattle, ACT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Phoenix, LSAT Test Prep in Chicago, ISEE Test Prep in Dallas Fort Worth, LSAT Test Prep in San Diego, SAT Test Prep in Chicago, SAT Test Prep in Boston, SAT 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

Calculus 2 : Parametric

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #3 : Derivatives Of Parametrics

Example Question #121 : Parametric, Polar, And Vector

Example Question #12 : Derivatives Of Parametrics

Example Question #121 : Parametric

Example Question #122 : Parametric, Polar, And Vector

Example Question #123 : Parametric, Polar, And Vector

Example Question #124 : Parametric, Polar, And Vector

Example Question #121 : Parametric

Example Question #125 : Parametric, Polar, And Vector

Example Question #126 : 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: