Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

Create An Account

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #381 : Spatial Calculus

The velocity function of a particle and a position of this particle at a known time are given by v(t)=27sin^3(t^3) and p(0)=3 . Approximate p(3) using Euler's Method and three steps.

Possible Answers:

45.24

-22.91

19.09

-72.71

-33.08

Correct answer:

45.24

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told v(t)=27sin^3(t^3) and p(0)=3

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{3-0}{3}=1$

p_0=3;t_0=0

p_1=3+(1)27sin^3(0^3)=3

p_2=3+(1)27sin^3(1^3)=19.09

p_3=19.09+(1)27sin^3(2^3)=45.24

Report an Error

Example Question #382 : Calculus

The velocity function of a particle and a position of this particle at a known time are given by $v(t)=\frac{sin(t^3)}{6}$ and $p(\pi)=0$ . Approximate $p(4\pi)$ using Euler's Method and three steps.

Possible Answers:

-0.660

-0.138

0.384

-0.209

Correct answer:

0.384

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told $v(t)=\frac{sin(t^3)}{6}$ and $p(\pi)=0$

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{4\pi-\pi}{3}=\pi$

$p_0=0;t_0=\pi$

$p_1=0+(\pi)\frac{sin(\pi^3)}{6}=-0.209$

$p_2=-0.209+(\pi)\frac{sin((2\pi)^3)}{6}=-0.138$

$p_3=-0.138+(\pi)\frac{sin((3\pi)^3)}{6}=0.384$

Report an Error

Example Question #382 : Spatial Calculus

The position of a t=4 is given by the following functions:

p(t) = 2t + 3

Find the velocity.

Possible Answers:

Answer not listed

Correct answer:

Explanation:

In order to find the velocity of a certain point, you first find the derivative of the position function to get the velocity function: p'(t) = v(t)

In this case, the position function is: p(t) = 2t + 3

Then take the derivative of the position function to get the velocity function: v(t) = 2

Then, plug t=4 into the velocity function: v(4) = 2

Therefore, the answer is:

Report an Error

Example Question #383 : Spatial Calculus

The position of a t=2 is given by the following functions:

$p(t) = - \cos(3t - 6)$

Find the velocity.

Possible Answers:

Answer not listed

Correct answer:

Explanation:

In order to find the velocity of a certain point, you first find the derivative of the position function to get the velocity function: p'(t) = v(t)

In this case, the position function is: $p(t) = - \cos(3t - 6)$

Then take the derivative of the position function to get the velocity function: $v(t) = 3\sin(3t - 6)$

Then, plug t=2 into the velocity function: $v(2) = 3\sin(3({\color{Blue} 2}) - 6)$

Therefore, the answer is:

Report an Error

Example Question #381 : Velocity

The position of a t=1 is given by the following functions:

p(t) = ln(4t^2 + 6t)

Find the velocity.

Possible Answers:

Answer not listed

$\frac{5}{7}$

$\frac{2}{5}$

$\frac{7}{5}$

$\frac{3}{4}$

Correct answer:

$\frac{7}{5}$

Explanation:

In order to find the velocity of a certain point, you first find the derivative of the position function to get the velocity function: p'(t) = v(t)

In this case, the position function is: p(t) = ln(4t^2 + 6t)

Then take the derivative of the position function to get the velocity function: $v(t) = \frac{8t + 6}{4t^2+6t}$

Then, plug t=1 into the velocity function: $v(1) = \frac{8({\color{Blue} 1})+ 6}{4({\color{Blue} 1})^2+6({\color{Blue} 1})}$

Therefore, the answer is: $\frac{7}{5}$

Report an Error

Example Question #382 : Velocity

The position of a t=0 is given by the following function:

$p(t) = e^{3t-ln(7)}$

Find the velocity.

Possible Answers:

Answer not listed

$\frac{6}{7}$

$\frac{4}{7}$

$\frac{3}{7}$

$\frac{1}{7}$

Correct answer:

$\frac{3}{7}$

Explanation:

In order to find the velocity of a certain point, you first find the derivative of the position function to get the velocity function: p'(t) = v(t)

In this case, the position function is: $p(t) = e^{3t-ln(7)}$ = $p(t) = \frac{e^{3t}}{7}$

Then take the derivative of the position function to get the velocity function: $v(t) = \frac{3e^{3t}}{7}$

Then, plug t=0 into the velocity function: $v(0) = \frac{3e^{3({\color{Blue} 0})}}{7}$

Therefore, the answer is: $\frac{3}{7}$

Report an Error

Example Question #381 : Calculus

The position of a t=2 is given by the following function:

p(t) = 4t^2 - e^t

Find the velocity.

Possible Answers:

Answer not listed

6.1

8.4

5.3

8.6

Correct answer:

8.6

Explanation:

In order to find the velocity of a certain point, you first find the derivative of the position function to get the velocity function: p'(t) = v(t)

In this case, the position function is: p(t) = 4t^2 - e^t

Then take the derivative of the position function to get the velocity function: v(t) = 8t - e^t

Then, plug t=2 into the velocity function: $v(2) = 8({\color{Blue} 2}) - e^{{\color{Blue} 2}}$

Therefore, the answer is: 8.6

Report an Error

Example Question #386 : Velocity

The position of a t=0 is given by the following function:

$p(t) = ln(3t + \sin(3t))$

Find the velocity.

Possible Answers:

Undefined

Answer not listed

Correct answer:

Undefined

Explanation:

In order to find the velocity of a certain point, you first find the derivative of the position function to get the velocity function: p'(t) = v(t)

In this case, the position function is: $p(t) = ln(3t + \sin(3t))$

Then take the derivative of the position function to get the velocity function: $v(t) = \frac{3+ 3\cos(3t)}{3t + \sin(3t)}$

Then, plug t=0 into the velocity function: $v(0) = \frac{3+ 3\cos(3({\color{Blue} 0}))}{3({\color{Blue} 0}) + \sin(3({\color{Blue} 0}))}$

Therefore, the answer is: Undefined

Report an Error

Example Question #382 : Calculus

Given the position function of a projectile in meters, find the velocity of the object at t=3 seconds.

s(t)=4t^2-8t+3

Possible Answers:

4 m/s

None of the other answers.

20 m/s

15 m/s

16 m/s

Correct answer:

16 m/s

Explanation:

The velocity of the projectile at any given point in time is modeled by the first derivative of the position function.

s'(t)=8t-8=v(t)=velocity

The velocity of the projectile at t=3 is then

v(3)=s'(3)=8(3)-8= 24-8=16 m/s

Report an Error

Example Question #382 : How To Find Velocity

Given the following position function, determine the velocity, , when t=2 :

S(t)= t^3 + 5t

Possible Answers:

V(2)= 21

V(2)=16

V(2)= 15

V(2)=17

Correct answer:

V(2)=17

Explanation:

The velocity can be determined at any given time by taking the first derivative of the position function.

In this case, the derivative of

S(t)=t^3+5t

is the velocity function

V(t)= 3t^2+5 ,

using the power rule

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

The next step is to substitute 2 into the velocity equation for t, and solving to obtain,

V(t)= 3t^2+5

$\\V(2)= 3(2)^2+5 \\V(2)=3(4)+5 \\V(2)=12+5$

V(2)= 17

Report an Error

View Calculus Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View Calculus Tutors

Joseph
Certified Tutor

University of Houston, Bachelor of Science, Biology, General.

View Calculus Tutors

Samuel
Certified Tutor

York University, Bachelor, Physics. York University, Master's/Graduate, Mathematics and Statistics.

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Miami, GRE Tutors in Chicago, ACT Tutors in New York City, GMAT Tutors in Atlanta, Algebra Tutors in Houston, Physics Tutors in Phoenix, GMAT Tutors in Boston, Spanish Tutors in Philadelphia, Physics Tutors in Washington DC, MCAT Tutors in New York City

Popular Courses & Classes

ACT Courses & Classes in Phoenix, SSAT Courses & Classes in Houston, GMAT Courses & Classes in Chicago, SSAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Denver, ISEE Courses & Classes in Seattle, GMAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Miami, GMAT Courses & Classes in Phoenix, MCAT Courses & Classes in Atlanta

Popular Test Prep

GRE Test Prep in Atlanta, SAT Test Prep in Miami, ACT Test Prep in San Francisco-Bay Area, ACT Test Prep in Phoenix, ACT Test Prep in Los Angeles, MCAT Test Prep in Dallas Fort Worth, GRE Test Prep in Philadelphia, GRE Test Prep in Seattle, GRE Test Prep in San Diego, GMAT 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 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #381 : Spatial Calculus

Example Question #382 : Calculus

Example Question #382 : Spatial Calculus

Example Question #383 : Spatial Calculus

Example Question #381 : Velocity

Example Question #382 : Velocity

Example Question #381 : Calculus

Example Question #386 : Velocity

Example Question #382 : Calculus

Example Question #382 : How To Find Velocity

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: