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 #311 : Spatial Calculus

The velocity function of a particle and a position of this particle at a known time are given by $v(t)=cos(\sqrt[5]{t})$ p(0)=0 . Approximate p(9) using Euler's Method and three steps.

Possible Answers:

0.958

1.376

3.958

4.376

Correct answer:

4.376

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 $v(t)=cos(\sqrt[5]{t})$ p(0)=0

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

$\Delta t = \frac{9-0}{3}=3$

p_0=0;t_0=0

$p_1=0+(3)cos(\sqrt[5]{0})=3$

$p_2=3+(3)cos(\sqrt[5]{3})=3.958$

$p_3=3.958+(3)cos(\sqrt[5]{6})=4.376$

Report an Error

Example Question #312 : Spatial Calculus

The velocity function of a particle and a position of this particle at a known time are given by v(t)=csc^3(t^2) p(1)=2 . Approximate p(1.6) using Euler's Method and three steps.

Possible Answers:

3.459

2.794

2.541

2.336

3.021

Correct answer:

2.794

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)=csc^3(t^2) p(1)=2

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

$\Delta t = \frac{1.6-1}{3}=0.2$

p_0=2;t_0=1

p_1=2+(0.2)csc^3(1^2)=2.336

p_2=2.336+(0.2)csc^3(1.2^2)=2.541

p_3=2.541+(0.2)csc^3(1.4^2)=2.794

Report an Error

Example Question #311 : Calculus

The velocity function of a particle and a position of this particle at a known time are given by v(t)=sin(4t^4) p(1.1)=0 . Approximate p(1.4) using Euler's Method and three steps.

Possible Answers:

-0.065

0.049

-0.091

0.083

-0.042

Correct answer:

-0.042

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)=sin(4t^4) p(1.1)=0

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

$\Delta t = \frac{1.4-1.1}{3}=0.1$

p_0=0;t_0=1.1

p_1=0+(0.1)sin(4(1.1)^4)=-0.041

p_2=-0.041+(0.1)sin(4(1.2)^4)=0.049

p_3=0.049+(0.1)sin(4(1.3)^4)=-0.042

Report an Error

Example Question #312 : Velocity

The velocity function of a particle and a position of this particle at a known time are given by v(t)=5sin(t^3-t^2) p(1)=0 . Approximate p(7) using Euler's Method and three steps.

Possible Answers:

-9.543

-6.904

-15.251

-7.625

-13.808

Correct answer:

-15.251

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)=5sin(t^3-t^2) p(1)=0

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

$\Delta t = \frac{7-1}{3}=2$

p_0=0;t_0=1

p_1=0+(2)(5sin(1^3-1^2))=0

p_2=0+(2)(5sin(2^3-2^2))=-7.568

p_3=-7.568+(2)(5sin(4^3-4^2))=-15.251

Report an Error

Example Question #313 : Velocity

The velocity function of a particle and a position of this particle at a known time are given by v(t)=cos(t^4-t) p(0)=0 . Approximate p(3) using Euler's Method and three steps.

Possible Answers:

1.137

0.137

4.137

3.137

2.137

Correct answer:

2.137

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)=cos(t^4-t) p(0)=0

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=0;t_0=0

p_1=0+(1)cos(0^4-0)=1

p_2=1+(1)cos(1^4-1)=2

p_3=2+(1)cos(2^4-2)=2.137

Report an Error

Example Question #314 : Velocity

The velocity function of a particle and a position of this particle at a known time are given by $v(t)=1.2^{t^3-t^2}$ p(0)=4 . Approximate p(3) using Euler's Method and three steps.

Possible Answers:

7.702

8.073

9.702

6.073

Correct answer:

8.073

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 $v(t)=1.2^{t^3-t^2}$ p(0)=4

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=4;t_0=0

$p_1=4+(1)1.2^{0^3-0^2}=5$

$p_2=5+(1)1.2^{1^3-1^2}=6$

$p_3=6+(1)1.2^{2^3-2^2}=8.073$

Report an Error

Example Question #315 : Velocity

The velocity function of a particle and a position of this particle at a known time are given by v(t)=2t^3 p(0)=0 . Approximate p(0.9) using Euler's Method and three steps.

Possible Answers:

0.2358

0.1458

0.1296

0.0162

0.3393

Correct answer:

0.1458

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)=2t^3 p(0)=0

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

$\Delta t = \frac{0.9-0}{3}=0.3$

p_0=0;t_0=0

p_1=0+(0.3)2(0)^3=0

p_2=0+(0.3)2(0.3)^3=0.0162

p_3=0.0162+(0.3)2(0.6)=0.1458

Report an Error

Example Question #316 : Velocity

The velocity function of a particle and a position of this particle at a known time are given by v(t)=t! p(1)=8 . Approximate p(4) using Euler's Method and three steps.

Possible Answers:

Correct answer:

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)=t! p(1)=8

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

$\Delta t = \frac{4-1}{3}=1$

p_0=8;t_0=1

p_1=8+(1)1!=9

p_2=9+(1)2!=11

p_3=11+(1)3!=17

Report an Error

Example Question #319 : Calculus

The velocity function of a particle and a position of this particle at a known time are given by $v(t)=cos(\pi t!)$ p(1)=0 . Approximate p(10) using Euler's Method and three steps.

Possible Answers:

Correct answer:

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 $v(t)=cos(\pi t!)$ p(1)=0

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

$\Delta t = \frac{10-1}{3}=3$

p_0=0;t_0=1

$p_1=0+(3)cos(\pi (1)!)=-3$

$p_2=-3+(3)cos(\pi (3)!)=0$

$p_3=0+(3)cos(\pi (6)!)=3$

Report an Error

Example Question #317 : Velocity

The velocity function of a particle and a position of this particle at a known time are given by $v(t)=sin^2(\frac{\pi}{3}t!)$ p(1)=2 . Approximate p(4) using Euler's Method and three steps.

Possible Answers:

$\frac{11}{7}$

$\frac{11}{4}$

$\frac{7}{2}$

$\frac{11}{2}$

$\frac{7}{4}$

Correct answer:

$\frac{7}{2}$

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 $v(t)=sin^2(\frac{\pi}{3}t!)$ p(1)=2

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

$\Delta t = \frac{4-1}{3}=1$

p_0=2;t_0=1

$p_1=2+(1)sin^2(\frac{\pi}{3}(1)!)=\frac{11}{4}$

$p_2=\frac{11}{4}+(1)sin^2(\frac{\pi}{3}(2)!)=\frac{7}{2}$

$p_3=\frac{7}{2}+(1)sin^2(\frac{\pi}{3}(3)!)=\frac{7}{2}$

Report an Error

View Calculus Tutors

Nicholas
Certified Tutor

Bryant University, Bachelor of Science, Actuarial Science.

View Calculus Tutors

Muhammad
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Mechanical Engineering.

View Calculus Tutors

Mykalin
Certified Tutor

Worcester Polytechnic Institute, Bachelor of Science, Astrophysics. Worcester Polytechnic Institute, Master of Science, Nucle...

All Calculus 1 Resources

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

Popular Subjects

Algebra Tutors in Phoenix, Math Tutors in Miami, French Tutors in Houston, SSAT Tutors in Washington DC, Algebra Tutors in New York City, Statistics Tutors in Miami, Chemistry Tutors in Phoenix, Biology Tutors in Washington DC, SSAT Tutors in Houston, Computer Science Tutors in Los Angeles

Popular Courses & Classes

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

Popular Test Prep

SSAT Test Prep in Atlanta, SAT Test Prep in Miami, ISEE Test Prep in Chicago, MCAT Test Prep in Boston, MCAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in San Diego, MCAT Test Prep in Denver, MCAT Test Prep in Chicago, MCAT Test Prep in Phoenix, SSAT 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 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #311 : Spatial Calculus

Example Question #312 : Spatial Calculus

Example Question #311 : Calculus

Example Question #312 : Velocity

Example Question #313 : Velocity

Example Question #314 : Velocity

Example Question #315 : Velocity

Example Question #316 : Velocity

Example Question #319 : Calculus

Example Question #317 : Velocity

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: