Call Now to Set Up Tutoring:

(888) 888-0446

AP Calculus BC : Euler's Method and L'Hopital's Rule

Study concepts, example questions & explanations for AP Calculus BC

Create An Account

All AP Calculus BC Resources

2 Diagnostic Tests 86 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 Next →

Example Question #31 : Euler's Method And L'hopital's Rule

$\begin{align*}&\text{The expression of a particular function is unknown;}\\&\text{however, we have an expression for its derivative.}\\&\text{Knowing that }f'(x)=tan(x)\text{ and }f(3)=12\\&\text{Approximate } f(21)\text{ using Euler's Method and }4\text{ steps.}\end{align*}$

Possible Answers:

11.36

100.94

10.47

8.41

25.23

Correct answer:

25.23

Explanation:

$\begin{align*}&\text{The general form of Euler's method, when a derivative function,}\\&\text{initial value, and step size are known, is:}\\&y_n=y_{n+1} +\Delta x f'(x_n,y_n)\\&\text{To calculate the step size find the distance between the final}\\&\text{and initial value and divide by the number of steps to be used:}\\&\Delta x = \frac{x_f-x_i}{Steps}\\&\text{For this problem, we are told: }f'(x)=tan(x);f(3)=12\\&\text{Knowing this, we may take the steps to estimate our function}\\&\text{value at our final x value:}\\&\Delta x = \frac{21-(3)}{4}=4.5\\&y_0=12;x_0=3\\&y_{1}=12+(4.5)(tan{(3)})=11.36\\&y_{2}=11.36+(4.5)(tan{(7.5)})=23.54\\&y_{3}=23.54+(4.5)(tan{(12)})=20.67\\&y_{4}=20.67+(4.5)(tan{(16.5)})=25.23\\&\\&\end{align*}$

Report an Error

Example Question #31 : Euler's Method And L'hopital's Rule

$\begin{align*}&\text{The expression of a particular function is unknown;}\\&\text{however, we have an expression for its derivative.}\\&\text{Knowing that }f'(x)=13sin(3x)\text{ and }f(2)=-15\\&\text{Approximate } f(11.4)\text{ using Euler's Method and }2\text{ steps.}\end{align*}$

Possible Answers:

25.92

-32.07

12.96

-10.45

103.68

Correct answer:

25.92

Explanation:

$\begin{align*}&\text{The general form of Euler's method, when a derivative function,}\\&\text{initial value, and step size are known, is:}\\&y_n=y_{n+1} +\Delta x f'(x_n,y_n)\\&\text{To calculate the step size find the distance between the final}\\&\text{and initial value and divide by the number of steps to be used:}\\&\Delta x = \frac{x_f-x_i}{Steps}\\&\text{For this problem, we are told: }f'(x)=13sin(3x);f(2)=-15\\&\text{Knowing this, we may take the steps to estimate our function}\\&\text{value at our final x value:}\\&\Delta x = \frac{11.4-(2)}{2}=4.7\\&y_0=-15;x_0=2\\&y_{1}=-15+(4.7)(13sin(3{(2)}))=-32.07\\&y_{2}=-32.07+(4.7)(13sin(3{(6.7)}))=25.92\\&\\&\end{align*}$

Report an Error

Example Question #31 : Euler's Method And L'hopital's Rule

$\begin{align*}&\text{The expression of a particular function is unknown;}\\&\text{however, we have an expression for its derivative.}\\&\text{Knowing that }f'(x)=-14cos(4x)\text{ and }f(-1)=17\\&\text{Approximate } f(7.6)\text{ using Euler's Method and }2\text{ steps.}\end{align*}$

Possible Answers:

56.35

7.84

2.61

15.67

9.62

Correct answer:

7.84

Explanation:

$\begin{align*}&\text{The general form of Euler's method, when a derivative function,}\\&\text{initial value, and step size are known, is:}\\&y_n=y_{n+1} +\Delta x f'(x_n,y_n)\\&\text{To calculate the step size find the distance between the final}\\&\text{and initial value and divide by the number of steps to be used:}\\&\Delta x = \frac{x_f-x_i}{Steps}\\&\text{For this problem, we are told: }f'(x)=-14cos(4x);f(-1)=17\\&\text{Knowing this, we may take the steps to estimate our function}\\&\text{value at our final x value:}\\&\Delta x = \frac{7.6-(-1)}{2}=4.3\\&y_0=17;x_0=-1\\&y_{1}=17+(4.3)(-14cos(4{(-1)}))=56.35\\&y_{2}=56.35+(4.3)(-14cos(4{(3.3)}))=7.84\\&\\&\end{align*}$

Report an Error

Example Question #34 : Euler's Method And L'hopital's Rule

$\begin{align*}&\text{The expression of a particular function is unknown;}\\&\text{however, we have an expression for its derivative.}\\&\text{Knowing that }f'(x)=-6x^{2}\text{ and }f(-1)=-20\\&\text{Approximate } f(11.9)\text{ using Euler's Method and }3\text{ steps.}\end{align*}$

Possible Answers:

-1816.97

-869.66

-363.39

-45.8

-9084.85

Correct answer:

-1816.97

Explanation:

$\begin{align*}&\text{The general form of Euler's method, when a derivative function,}\\&\text{initial value, and step size are known, is:}\\&y_n=y_{n+1} +\Delta x f'(x_n,y_n)\\&\text{To calculate the step size find the distance between the final}\\&\text{and initial value and divide by the number of steps to be used:}\\&\Delta x = \frac{x_f-x_i}{Steps}\\&\text{For this problem, we are told: }f'(x)=-6x^{2};f(-1)=-20\\&\text{Knowing this, we may take the steps to estimate our function}\\&\text{value at our final x value:}\\&\Delta x = \frac{11.9-(-1)}{3}=4.3\\&y_0=-20;x_0=-1\\&y_{1}=-20+(4.3)(-6{(-1)}^{2})=-45.8\\&y_{2}=-45.8+(4.3)(-6{(3.3)}^{2})=-326.76\\&y_{3}=-326.76+(4.3)(-6{(7.6)}^{2})=-1816.97\\&\\&\end{align*}$

Report an Error

Example Question #221 : Derivatives

$\begin{align*}&\text{The expression of a particular function is unknown;}\\&\text{however, we have an expression for its derivative.}\\&\text{Knowing that }f'(x)=-2cos(6x)\text{ and }f(-1)=-11\\&\text{Approximate } f(6.2)\text{ using Euler's Method and }4\text{ steps.}\end{align*}$

Possible Answers:

-36.81

-6.13

-14.46

-12.27

-12.76

Correct answer:

-12.27

Explanation:

$\begin{align*}&\text{The general form of Euler's method, when a derivative function,}\\&\text{initial value, and step size are known, is:}\\&y_n=y_{n+1} +\Delta x f'(x_n,y_n)\\&\text{To calculate the step size find the distance between the final}\\&\text{and initial value and divide by the number of steps to be used:}\\&\Delta x = \frac{x_f-x_i}{Steps}\\&\text{For this problem, we are told: }f'(x)=-2cos(6x);f(-1)=-11\\&\text{Knowing this, we may take the steps to estimate our function}\\&\text{value at our final x value:}\\&\Delta x = \frac{6.2-(-1)}{4}=1.8\\&y_0=-11;x_0=-1\\&y_{1}=-11+(1.8)(-2cos(6{(-1)}))=-14.46\\&y_{2}=-14.46+(1.8)(-2cos(6{(0.8)}))=-14.77\\&y_{3}=-14.77+(1.8)(-2cos(6{(2.6)}))=-11.19\\&y_{4}=-11.19+(1.8)(-2cos(6{(4.4)}))=-12.27\\&\\&\end{align*}$

Report an Error

← Previous 1 2 3 4 Next →

View AP Calculus BC Tutors

Gary
Certified Tutor

SUNY at Albany, Bachelor of Science, Economics. Pace University-New York, Masters in Business Administration, Analysis and Fu...

View AP Calculus BC Tutors

Shakeel
Certified Tutor

View AP Calculus BC Tutors

Andrew
Certified Tutor

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

All AP Calculus BC Resources

2 Diagnostic Tests 86 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Boston, Chemistry Tutors in Atlanta, Chemistry Tutors in Dallas Fort Worth, Statistics Tutors in Denver, Reading Tutors in Denver, SAT Tutors in Houston, LSAT Tutors in Los Angeles, Reading Tutors in Atlanta, Physics Tutors in Philadelphia, Math Tutors in Miami

Popular Courses & Classes

SAT Courses & Classes in Chicago, ACT Courses & Classes in Los Angeles, LSAT Courses & Classes in Washington DC, GMAT Courses & Classes in New York City, SSAT Courses & Classes in Miami, Spanish Courses & Classes in Denver, SSAT Courses & Classes in New York City, SSAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Houston

Popular Test Prep

ISEE Test Prep in Washington DC, MCAT Test Prep in San Diego, GMAT Test Prep in Seattle, GMAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Atlanta, MCAT Test Prep in Seattle, SAT Test Prep in Dallas Fort Worth, GRE Test Prep in Miami, GRE Test Prep in Los Angeles, SSAT Test Prep in Chicago

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

AP Calculus BC : Euler's Method and L'Hopital's Rule

Study concepts, example questions & explanations for AP Calculus BC

All AP Calculus BC Resources

Example Questions

Example Question #31 : Euler's Method And L'hopital's Rule

Example Question #31 : Euler's Method And L'hopital's Rule

Example Question #31 : Euler's Method And L'hopital's Rule

Example Question #34 : Euler's Method And L'hopital's Rule

Example Question #221 : Derivatives

All AP Calculus BC Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: