ISBN: 764586831. Definitions: The Taylor Series for a function f (x) around a center value a is the power series. 24 Power Series 25. AP Calculus AB covers basic introductions to limits, derivatives, and integrals. ISBN: 764586831. AP Calculus BC: Focusing on Taylor Series Questions 2021 AP Live Bryan Passwater & Tony Record ?) When 𝑥 = 1 2, the terms in the series for ℎ (𝑥) alternate in sign and decrease in magnitude to 0. is given by. Calculus BC: Series Math Study Guide Terms Topics Power Series We now investigate the convergence of power series, of which the Taylor series we will encounter in the next SparkNote are a special case. Calculus BC – 10. Differential Equations and Growth/Decay. I am currently enrolled in AP Calc AB and have been making straight A's and doing well, so I have that going for me, but that's about it - I'm going into this blind. 6 #13-31 odd, 47-57 odd, 103-104. AP Calculus BC Final Exam Review Project Unit 10 -Sequences & Series (Part 2) *Quiz (Days 1 - 5): Thursday, March 8th. Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. AP Calculus BC Taylor and Maclaurin Series FRQ 2. ln x is an extremely well-known example of a function that can NOT be a maclaurin series, I was just remarking why did Taylor have to take the . Video 12. Day 6 - Taylor Series (March 9th). Flamingo Math by Jean Adams. Answer: Let f(x) = √ x and evaluate the first few derivatives of f: f0(x) = 1 2 √ x f00(x) = − 1 4x3/2 f000(x) = 3 8x5/2 f(4)(x) = − 15 16x7/2 Therefore, f(1) = 1 f0(1) = 1 2 f00(1) = − 1 4 f000(1) = 3 8 f(4)(1) = − 15 16 Hence, the Taylor series. Is this an over or under approximation of sin(0. Part (d) asked students to use the Taylor series from part (c) to determine whether f has. This calculus 2 video tutorial explains how to find the Taylor series and the Maclaurin series of a function using a simple formula. Section 10. Harmonic Series -. Taylor Series Calculator Find the Taylor series representation of functions step-by-step full pad » Examples Related Symbolab blog posts Advanced Math Solutions – Ordinary Differential Equations Calculator <div class="p1"> Differential equations contain derivatives, solving the equation involves integration (to get. Start practicing—and saving your progress—now: https://www. Part (a) assessed students’ abilities to find the first four nonzero terms and the general term of the Taylor series for () 2 fx e= −x. Video 7. Example Question #5 : Ap Calculus Bc. So as long as x is in this interval, it's going to take on the same values as our original function, which is a pretty neat idea. AP Calculus BC Free-Response Question 5 College Board 2021 AP Exam Administration: Student Samples. Manipulation of Series. A Taylor series is a clever way to approximate any function as a polynomial with an infinite number of terms. Here’s the complete formula for the Taylor series of f, with center c ( Taylor’s Formula ): The Maclaurin series is the same thing, but with c = 0 plugged in. Taylor & Maclaurin polynomials (practice) | Khan Academy > Math > AP®︎/College Calculus BC Infinite sequences and series Taylor & Maclaurin polynomials Google Classroom f ( x) = − 4 x 3 + 3 x 2 − 6 x + 10 What is the coefficient for the term containing ( x − 3) 2 in the Taylor polynomial, centered at x = 3 , of f ? Choose 1 answer: − 33 A − 33 66 B. The Taylor Series represents f(x) on (a-r,a+r) if and only if. Visualizing Taylor series approximations (video) | Khan Academy Course: AP®︎/College Calculus BC > Unit 10 Geometric series interval of convergence Math > AP®︎/College Calculus BC > Infinite sequences and series > Finding Taylor or Maclaurin series for a function © 2023 Khan Academy Terms of use Privacy Policy Cookie Notice. Here is a set of notes used by Paul Dawkins to teach his Calculus II course at Lamar University. Show Solution. Publisher: Cliffs Notes. Visualizing Taylor series approximations Euler's formula & Euler's identity Geometric series interval of convergence Math > AP®︎/College Calculus BC > Infinite sequences and series > Finding Taylor or Maclaurin series for a function © 2023 Khan Academy Worked example: recognizing function from Taylor series Google Classroom About Transcript. Study concepts, example questions & explanations for AP Calculus BC. Flamingo Math by Jean Adams. AP Calculus BC, Part 2. (a) Let f x x2 sin. Inspired by the amazing circuits created by Virge Cornelius, who teaches AB calculus, I have created a circuit for BC calculus for series. WEAKNESS! From the 2003 BC Exam: 1. The Taylor Series, sometimes referred to as the Taylor Polynomial, allows us to find a polynomial function that approximates another function by first choosing a. In this article we will define Taylor. 10 Taylor series Khan Academy Taylor, Maclaurin, and Power series online quizzes (click):. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. n n n. In this section we will discuss how to find the Taylor/Maclaurin Series for a function. Although it would be possible to do this by computing. Taylor series are named after the British. The whole point in developing Taylor series is that they replace more complicated functions with polynomial-like expressions. Unit 3 Differentiation: composite, implicit, and inverse functions. 7 years ago. The AP Calculus BC Exam will have both paper and digital formats in 2021. In this AP Daily: Live Review session, we will review Taylor and Maclaurin polynomials and work several AP-style free-response and multiple-choice problems. is given by. To find the Maclaurin Series simply set your Point to zero (0). The series problem defined. Taylor & Maclaurin polynomials (practice) | Khan Academy > Math > AP®︎/College Calculus BC Infinite sequences and series Taylor & Maclaurin polynomials Google Classroom f ( x) = − 4 x 3 + 3 x 2 − 6 x + 10 What is the coefficient for the term containing ( x − 3) 2 in the Taylor polynomial, centered at x = 3 , of f ? Choose 1 answer: − 33 A − 33 66 B. If you want the Maclaurin polynomial, just set the point to 0. (c) Use the ratio test to find the interval of convergence for the Taylor series found in part (b). AP Calculus BC covers all AP Calculus AB topics plus additional topics (including integration by parts, Taylor series, parametric equations, vector calculus, and polar coordinate functions). A: Let the line x+y=b bisects the chord at point P (α, b-α). Write the general term of the Taylor series for about x = 0. (a) Write the third-degree Taylor polynomial for f about x = 5. On this page you will find selected tutorials, references. x = 0. Show that |ℎ ( 1 2) − 𝑃2(1 2)| < 1 40. Example: sine function. Flamingo Math by Jean Adams. be the function defined by (a) Write the first four nonzero terms and the general term of the Maclaurin series for. n f. Give a reason for your answer. You can expect to see several multiple choice questions and at least one free response question on. Calculus 3 is (possibly) in two parts. (b) Find the first three nonzero terms and the general term of the Taylor series for f', the derivative of f,. 1 / 4. It's going to be equal to any of the derivatives evaluated at 0. pdf: File Size: 271 kb: File Type: pdf: Download File. Euler's formula is eⁱˣ=cos (x)+i⋅sin (x), and Euler's Identity is e^ (iπ)+1=0. 2010 AP Calculus BC Exam #6. AP Calculus BC : Taylor Series Study concepts, example questions & explanations for AP Calculus BC. Identify and apply power series for the function f(x) = 1 1− x and related functions. The 2020 test will be given May 5, 2020. (a) Find the first four nonzero terms of the Taylor series about x = 0 for f x 1. Topics covered are Integration Techniques (Integration by Parts, Trig Substitutions, Partial Fractions, Improper Integrals), Applications (Arc Length, Surface Area, Center of Mass and Probability), Parametric Curves (inclulding various applications), Sequences, Series (Integral Test, Comparison. As such, you can do term-by-term differentiation and integration. (b) Use the result from part (a) to find the first four terms and the general term of the series expansion about x = 2 for ln 1x. Flamingo Math by Jean Adams. Google Classroom About Transcript A Taylor series is a clever way to approximate any function as a polynomial with an infinite number of terms. Write the second-degree Taylor polynomial for. Taylor and Maclaurin Series 26. While you will revisit parametric and polar coordinates when you do vector calculus, you’re hilariously wrong about BC being “mostly applications and tricks”. A Maclaurin series is the specific case of a Taylor series that is centered at c = 0, resulting in the simpler-looking series. geometric series is simply the sum of the rest of the terms of the series, which itself is a geometric series. While the differential equations applications are beyond the scope of this course there are some applications from a Calculus setting that we can look at. Brand new AP-style free-res. Some infinite series converge to a finite value. WORKSHEET 1 ON TAYLOR POLYNOMIALS. Addition of algebraic expressions worksheets Ato fortnightly tax calculator Best way to stop nightfall Calculate apparent power Chapter 3 maths class 10 examples Definition of limit in mathematics Dividing polynomials using synthetic division worksheet Find dy/dx if y 3x^4 Free calculators online Google verification code pc Home calculator sale How to create. Learn how to find a partial sum of a Taylor series for f(x) using a Taylor polynomial, and see examples that walk through. In order to ask if a power series converges, we must first specify the value of x. (b) The Taylor series for f about x — 1 has a radius of convergence of 2. AP CALCULUS (BC) NAME. Free AP Calculus AB/BC study guides for Unit 10 – Infinite Sequences & Series (BC Only). AP Calculus BC Skills Practice. Constructing a Taylor Series [edit | edit source] Several methods exist for the calculation of. Taylor's Formula with Remainder Let f(x) be a function such that f(n+1)(x) exists for all x on an open interval containing a. AP Calculus Taylor Series Student Handout Taylor series is a very important topic on the BC Exam. For the function values: f(−12) = 6;f′(−12) = 19;f′′(−12) = 18;f′′′(−12) = −2 Approximate f(−10) using a Taylor expansion. Taylor’s Theorem with Remainder Taylor’s Theorem is an existence theorem. State the ratio test. The Taylor Series is the name for the series approximation of functions, and it can be found by the following formula. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered. Start practicing—and saving your progress—now: https://www. The function g has derivatives of all orders, and the Maclaurin series for g is. Example Questions. Brookline High • MATH. Definition 11. Here is one such example. Practice Online AP Calculus BC : 10. A Taylor series is a clever way to approximate any function as a polynomial with an infinite number of terms. Don't all infinite series grow to infinity? It turns out the answer is no. You can expect to see several multiple choice questions and at least one free response question on. pdf (4. (c) Use the ratio test to find the interval of convergence for the Taylor series found in part (b). Manipulation of Series. 24 May 2021. the Taylor series from part (a) to write the first four nonzero terms and the general term of the Taylor series for f about x = 1. f(x) = 8*, a=3 Choose the. The zeroth derivative is just the function itself. We now investigate the convergence of power series, of which the Taylor series we will encounter in the next SparkNote are a special case. PLEASE REFRAIN FROM USING INSTRUMENTS OF. AP® Calculus BC 2005 Scoring Guidelines Form B The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. (a) Find the value of R. The general form of a Taylor series is, assuming the function and all its derivatives exist and are continuous on an interval centered at and containing. The n-th derivative evaluated at 0. Video 5. The function f is defined by the power series () ()() ( )2 0 11 1 1 1nn n fx x x x x = ∞ =+ + + + + + + + = +""∑ for all real numbers x for which the series converges. Student BC Manual (no solutions) in printed form. The Taylor series for a function f about x = I is given by E (—1) and converges to f (x) for Ix — Il < R where R is the radius of convergence of the Taylor series. The biggest topic in BC is sequences and series, Taylor series, convergence testing. We now investigate the convergence of power series, of which the Taylor series we will encounter in the next SparkNote are a special case. (c) Use the series in part (b) to compute a number that differs from 3 ln 2 by less than 0. 0 n n n f xaxc where the domain of f is the set of all x for which the power series converges. A Taylor series centered at a= 0 is specially named a Maclaurin series. Algebra is the study of structure (not to be confused with high school algebra). Free-Response Questions from the 2021 AP Calculus BC Exam Keywords: Calculus BC; Free-Response. Unit 3: Taylor and MacLaurin Series Homework Solutions: Building Series HW Download File building_a_series_hw_key. CHAPTER 9 REVIEW. Example Question #5 : Ap Calculus Bc. Start practicing—and saving your progress—now: https://www. Improve your scholarly performance. n n n n 0. Part (b). Section 8. ) Problem : Find the Taylor series for the function g(x) = 1/ about x = 1. (b) Use the Taylor series found in part (a) to write the first four nonzero terms and the general term of the Taylor series for f about x = 1. It's going to be equal to any of the derivatives evaluated at 0. A power series is a series of the form anxn where the an are constants and x is a variable. pdf doc ; CHAPTER 10 - Approximating Functions Using Series. And that's why it makes applying the Maclaurin series formula fairly straightforward. (a) Write the first four nonzero terms and the general term of the Taylor series for f about x = l. The AP Calculus BC Exam historically has a higher pass rate than other AP exams,. Then, for every x in the interval, where R n(x) is the remainder (or error). So our function, so our first derivative, f prime of x is just going to be, just gonna use the power rule a lot, six x to the fifth minus three x squared. of a function!. A power series is a series of the form. As we will see, the values for which a particular Taylor series converges can be given quite a simple characterization. CALCULUS BC 2014 SCORING GUIDELINES Question 6 The Taylor series for a function f about x = I is given by E (—1) x n=l Ix — Il < R, where R is the radius of convergence of the Taylor series. Start practicing—and saving your progress—now: https://www. Taylor polynomials are incredibly powerful for approximations and analysis. AP Calculus BC Infinite Series Multiple Choice 2. The series problem defined. 1) Problem Statement: What order Taylor polynomial is needed to . Topics: Series, Taylor Series, Taylor Polynomial, manipulating known series, Alternating Series Error. 1 ,5 1 f x n x _____ On problems 4 – 6, find a Taylor polynomial of degree n for each of the following. Part (a) assessed students’ abilities to find the first four nonzero terms and the general term of the Taylor series for () 2 fx e= −x. 2000- BC 3 The Taylor series about x = 5 for a certain function converges to f(x) for all x in the interval of convergence. Give a reason for your answer. In the case of a Maclaurin series, we're approximating this function around x is equal to 0, and a Taylor series, and we'll talk about that in a future video, you can pick an arbitrary x value - or f(x) value, we should say, around which to approximate the function. (a) Find the value of R. Step 2: Take the Taylor expansion formula for. Given that g 0 1, write the first five nonzero terms and the general term of the Taylor series for gx about x = 0. (b) Use the Taylor series for f about x =0 found in part (a) to determine whether f has a relative maximum, relative minimum, or neither at x =0. Here f (n) (a) represents the n-th derivative of f, with a plugged in. When creating the. In the case of a Maclaurin series, we're approximating this function around x is equal to 0, and a Taylor series, and we'll talk about that in a future video, you can pick an arbitrary x value - or f(x) value, we should say, around which to approximate the function. There are functions that are not equal to their Taylor series. Find Taylor/Maclaurin series step by step. (b) Let g x xc 2 sin. This method has application in many engineering fields. Given that g 0 1, write the first five nonzero terms and the general term of the Taylor series for gx about x = 0. Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. That being said these are probably the hardest 3 units in the BC course (especially series) so make sure to study them well. Take the center aclose to x, giving small (x a) and tiny (x a)n. AP Calculus BC. It's going to be equal to any of the derivatives evaluated at 0. Explore the concepts, methods, and applications of differential and integral calculus, including topics such as parametric, polar, and vector functions, and series. Graph yl = sinx and Y2 x — 31 51. 2011 BC 6 a b (Form B) 7. In a general sense, for any given n, there is no better bound. 9), you can use Taylor series to calculate its value at some in-between point (e. Visualizing Taylor series approximations (video) | Khan Academy Course: AP®︎/College Calculus BC > Unit 10 Geometric series interval of convergence Math > AP®︎/College Calculus BC > Infinite sequences and series > Finding Taylor or Maclaurin series for a function © 2023 Khan Academy Terms of use Privacy Policy Cookie Notice. Study concepts, example questions & explanations for AP Calculus BC. com/sign-up?referrer_code=1002For notes, practice problems, and more les. Fill in the blank: 11 1 23 4 23 4. Part (b). The first three non-zero terms in the Taylor series about x = 0 for f(x) = cos x are A. Taylor & Maclaurin polynomials (practice) | Khan Academy > Math > AP®︎/College Calculus BC Infinite sequences and series Taylor & Maclaurin polynomials Google Classroom f ( x) = − 4 x 3 + 3 x 2 − 6 x + 10 What is the coefficient for the term containing ( x − 3) 2 in the Taylor polynomial, centered at x = 3 , of f ? Choose 1 answer: − 33 A − 33 66 B. Courses on Khan Academy are always 100% free. Give a reason for your answer. AP Calculus AB covers basic introductions to limits, derivatives, and integrals. hot boy sex
(b) Find the first three nonzero terms and the general term of the Taylor series for f', the derivative of f,. . Taylor series calc bc
A Taylor series is a clever way to approximate any function as a polynomial with an infinite number of terms. You’re also leaving our parametric and polar functions and the calculus of them. AP Calculus BC covers all AP Calculus AB topics plus additional topics (including integration by parts, Taylor series, parametric equations, vector calculus, and polar coordinate functions). Create An Account Create Tests & Flashcards. AP Calculus BC: Focusing on Taylor Series Questions2021 AP LiveBryan Passwater & Tony RecordCalculus BC - 2021 AP Live Review Session 1Focusing on Taylor . (b) Use the result from part (a) to find the first four terms and the general term of the series expansion about x = 2 for ln 1x. AP Calculus BC covers all AP Calculus AB topics plus additional topics (including integration by parts, Taylor series, parametric equations, vector calculus, and polar coordinate functions). 2014 CALCULUS BC FREE-RESPONSE QUESTIONS 6. For most functions, we assume the function is equal to its Taylor series on the series' interval of convergence and only use Theorem 77 when we suspect something may not work as expected. • If you have a table of values of a function (e. As we will see, the values for which a particular Taylor series converges can be given quite a simple characterization. This section provides the list of Taylor's series of some common functions as Exponential function, Natural logarithm. Remember, a Taylor series for a function f, with center c, is:. x =. As title says, I have decided to self-study AP Calc BC starting today, 2 months out from exams. Here is a set of practice problems to accompany the Taylor Series section of the Series & Sequences chapter of the notes for Paul Dawkins Calculus II course at Lamar University. Use this series and the series for sine of x squared, found in part A, to write the first four non-zero terms of the Taylor series for f-- so, for this f right over here-- about x equals 0. AP Calculus BC: Focusing on Taylor Series Questions 2021 AP Live Bryan Passwater & Tony Record ?) When 𝑥 = 1 2, the terms in the series for ℎ (𝑥) alternate in sign and decrease in magnitude to 0. Differentiate the above and get f0(x) = 2+4x+8x2 + +2n+1xn+ = X1 n=0 2n+1xn: (c)Use the Maclaurin series you found in part (b) to find the value. To determine if [latex]R_{n}[/latex]. Taylor’s series method: The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and all of its derivatives,. AP Calculus BC : Taylor Series Study concepts, example questions & explanations for AP Calculus BC. Sequences and series are used to study the behavior of infinite sums of numbers. What is the polynomial approximation for the value of sin 1 obtained by using the fifth-degree Taylor polynomial about . f x e n3 x,4 2. AP Calculus BC Free-Response Question 5 College Board 2021 AP Exam Administration: Student Samples. CALCULUS BC. AP Calculus BC Review: Taylor Polynomials. How can we determine whether a function does have a power series. Example Question #5 : Ap Calculus Bc. Plus, join AP exam season live streams &. Convergence Issues Because there are an infinite number of terms in a typical Taylor series, we have to address questions of convergence. (d) Use the Taylor series for f about 1x = to determine whether the graph of f has any points of. com/sign-up?referrer_code=1002For notes, . We also derive some well known formulas for Taylor series of e^x , cos(x) and sin(x) around x=0. x () about. SERIES (BC Topic) 1. Create An Account Create Tests & Flashcards. Video 4. Unit 3: Taylor and MacLaurin Series Homework Solutions: Building Series HW Download File building_a_series_hw_key. Part (a) asked for the first four nonzero terms of the Taylor series for sin x about x =0 and also for the first four nonzero terms of the Taylor series for sin(x2 ) about x =0. (b) The Taylor series for f about x — 1 has a radius of convergence of 2. As such, you can do term-by-term differentiation and integration. In order to ask if a power series converges, we must first specify the value of x. Authors: Dale W Johnson, Kerry J King. Taylor series is a very important topic on the BC Exam. 10 Taylor series Khan Academy Taylor, Maclaurin, and Power series online quizzes (click):. Show that |ℎ ( 1 2) − 𝑃2(1 2)| < 1 40. X equals zero. So to have an infinite Taylor polynomial, a function must be differentiable infinitely many times. The most common test to find the interval of convergence for. In this section we will discuss how to find the Taylor/Maclaurin Series for a function. Chapter 10 : Series and Sequences. ” stand for “anno domini,” meaning “in the year of our Lord,” according to How Stuff Works. AP Calculus BC Taylor and Maclaurin Series FRQ 2. SERIES (BC Topic) 1. I am currently enrolled in AP Calc AB and have been making straight A's and doing well, so I have that going for me, but that's about it - I'm going into this blind. (c) The Taylor series for f about x I can be used to represent f(l. 8: POWER SERIES, pg. We will therefore, spend a little time on sequences as well. Liberty BC Calculus Day 0: 2/11 and 2/12 - L'Hop and Improper Integrals Day 1: 2/13 and 2/18 - 9. AP® CALCULUS BC 2007 SCORING COMMENTARY Question 6 Overview This problem dealt with Taylor series. Suppose ƒ (x) = ∑ c (n) (x - a)ⁿ is a power series about the point a with radius of convergence R > 0, i. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Taylor's Formula with Remainder Let f(x) be a function such that f(n+1)(x) exists for all x on an open interval containing a. Deepen your understanding of math and physics by taking AP Calculus BC. of a function!. Unit 4 Contextual applications of differentiation. 1: Maclaurin and Taylor series. Example Questions. Now integrate both sides of the equation and you get: Sum from n=1 to infinity of (x n )/n = -log (1-x). 2021 Live Review 1 | AP Calculus BC | Focusing on Taylor Series Questions Advanced Placement 275K subscribers Subscribe 68K views Streamed 1 year ago In this AP Daily: Live Review session for. Let 1 1 ( ) x f x. Use an 8th degree Taylor polynomial to approximate. Don't all infinite series grow to infinity? It turns out the answer is no. Only $14. Today, the membership association is. This site contains miscellaneous resources for students and teachers of Advanced Placement Calculus AB and BC. C (AP Calculus Course and Exam Description, BC Sample 8) DL:3 f(0) 3 f (0) 1!. AP Calculus BC covers all AP Calculus AB topics plus additional topics (including integration by parts, Taylor series, parametric equations, vector calculus, and polar coordinate functions). Cliffs AP:. Since they gave us the Taylor polynomial formula, . You can prove this to yourself by constructing examples where E (x) is exactly equal to the bound shown in the video. 8: POWER SERIES, pg. whose graph is the tangent line (Calculus I x2. 2011 BC 6 a b (Form B) 7. Course Description: • Calculus BC is a full-year course in the calculus of functions of a single variable. 2) as an alternating series. AP Calculus AB covers basic introductions to limits, derivatives, and integrals. Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform. State the definition of a Taylor series. fx x x( )= +sin cos(2 ) and provided (a graph of y fx= (5) ). In this article we will define Taylor. a0 + a1x +. tangent line approximation. Manipulation of Series. It is known that ( )1. Problem Set: Taylor and Maclaurin Series. Then, for every x in the interval, where R n(x) is the remainder (or error). 2016 AP Calculus BC Exam Free Response Question #6The Series question! Write four nonzero terms of a Taylor polynomial and the general term. Therefore the interval of convergence is -1 < x ≤ 1. • If you have a table of values of a function (e. AP Calculus BC-3 2000 The Taylor series about a; 5 for a certain function f converges to for all in the interval of convergence. Definitions: The Taylor Series for a function f (x) around a center value a is the power series. . sendnudesx mega, little alchemy unblocked, check porn stars, faceswap porn, pittsfield ma craigslist, kc calculations chemsheets answers a2 008, mcdonalds batman, flmbokep, stepsister free porn, brooke monk nudes twitter, gm overwatch, the wiggles 2000 co8rr