CALCULUS
11th Edition
ISBN: 9781337761512
Author: Larson
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter P.1, Problem 12E
Sketching a Graph by Point Plotting In Exercises 7–16, sketch the graph of the equation by point plotting.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
#3 Find the derivative y' = of the following functions, using the derivative rules:
dx
a) y-Cos 6x b) y=x-Sin4x c) y=x-Cos3x d) y=x-R CD-X:-:TCH :D:D:D - Sin
f)
Sin(x²) (9) Tan (x³)
mate
hat is the largest area that can be en
18 For the function y=x³-3x² - 1, use derivatives to:
(a) determine the intervals of increase and decrease.
(b) determine the local (relative) maxima and minima.
(c) determine the intervals of concavity.
(d) determine the points of inflection.
b)
(e) sketch the graph with the above information indicated on the graph.
use L'Hopital Rule to evaluate the following.
a) 4x3 +10x2
23009׳-9
943-9
b) hm
3-84
хто бу+2
< xan
x-30650)
Chapter P Solutions
CALCULUS
Ch. P.1 - Finding Intercepts Describe how to find the x- and...Ch. P.1 - CONCEPT CHECK Verifying Points of Intersection How...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Prob. 7ECh. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Prob. 10E
Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Prob. 14ECh. P.1 - Prob. 15ECh. P.1 - Prob. 16ECh. P.1 - Approximating Solution Points Using Technology In...Ch. P.1 - Approximating Solution Points Using Technology In...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Prob. 22ECh. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Finding Intercepts In Exercises 19-28, find any...Ch. P.1 - Prob. 29ECh. P.1 - Prob. 30ECh. P.1 - Prob. 31ECh. P.1 - Prob. 32ECh. P.1 - Prob. 33ECh. P.1 - Prob. 34ECh. P.1 - Prob. 35ECh. P.1 - Prob. 36ECh. P.1 - Prob. 37ECh. P.1 - Prob. 38ECh. P.1 - Prob. 39ECh. P.1 - Prob. 40ECh. P.1 - Prob. 41ECh. P.1 - Prob. 42ECh. P.1 - Prob. 43ECh. P.1 - Prob. 44ECh. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Prob. 46ECh. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Prob. 48ECh. P.1 - Prob. 49ECh. P.1 - Prob. 50ECh. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Prob. 53ECh. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Prob. 55ECh. P.1 - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P.1 - Finding Points of Intersection In Exercises 57-62....Ch. P.1 - Finding Points of Intersection In Exercises 57-62....Ch. P.1 - Finding Points of Intersection In Exercises 57-62....Ch. P.1 - Finding Points of Intersection In Exercises 57-62,...Ch. P.1 - Prob. 61ECh. P.1 - Finding Points of Intersection In Exercises 57-62....Ch. P.1 - Finding Points of Intersection Using Technology In...Ch. P.1 - Prob. 64ECh. P.1 - Prob. 65ECh. P.1 - Finding Points of Intersection Using Technology In...Ch. P.1 - Modeling Data The table shows the Gross Domestic...Ch. P.1 - Prob. 68ECh. P.1 - Break-Even Point Find the sales necessary to break...Ch. P.1 - Using Solution Points For what values of k does...Ch. P.1 - EXPLORING CONCEPTS Using Intercepts Write an...Ch. P.1 - EXPLORING CONCEPTS Symmetry A graph is symmetric...Ch. P.1 - Prob. 73ECh. P.1 - HOW DO YOU SEE IT? Use the graphs of the two...Ch. P.1 - True or False ? In Exercises 75-78, determine...Ch. P.1 - Prob. 76ECh. P.1 - True or False? In Exercises 75-78, determine...Ch. P.1 - True or False? In Exercises 75-78, determine...Ch. P.2 - Slope-Intercept Form In the form y = mx + b, what...Ch. P.2 - Perpendicular Lines Is it possible for two lines...Ch. P.2 - Estimating Slope In Exercises 36, estimate the...Ch. P.2 - Prob. 4ECh. P.2 - Prob. 5ECh. P.2 - Prob. 6ECh. P.2 - Prob. 7ECh. P.2 - Finding the Slope of a Line In Exercises 7-12,...Ch. P.2 - Finding the Slope of a Line In Exercises 7-12,...Ch. P.2 - Finding the Slope of a Line In Exercises 7-12,...Ch. P.2 - Finding the Slope of a Line In Exercises 7-12,...Ch. P.2 - Finding the Slope of a Line In Exercises 7-12,...Ch. P.2 - Sketching Lines In Exercises 13 and 14. sketch the...Ch. P.2 - Sketching Lines In Exercises 13 and 14, sketch the...Ch. P.2 - Prob. 15ECh. P.2 - Finding Points on a Line In Exercises 1518, use...Ch. P.2 - Prob. 17ECh. P.2 - Finding Points on a Line In Exercises 1518, use...Ch. P.2 - Finding an Equation of a Line In Exercises 19-24,...Ch. P.2 - Prob. 20ECh. P.2 - Prob. 21ECh. P.2 - Prob. 22ECh. P.2 - Prob. 23ECh. P.2 - Prob. 24ECh. P.2 - Prob. 25ECh. P.2 - Prob. 26ECh. P.2 - Prob. 27ECh. P.2 - Prob. 28ECh. P.2 - Prob. 29ECh. P.2 - Finding the Slope and y-Intercept In Exercises...Ch. P.2 - Prob. 31ECh. P.2 - Prob. 32ECh. P.2 - Prob. 33ECh. P.2 - Prob. 34ECh. P.2 - Sketching a Line in the Plane In Exercises 35-42,...Ch. P.2 - Prob. 36ECh. P.2 - Prob. 37ECh. P.2 - Prob. 38ECh. P.2 - Prob. 39ECh. P.2 - Prob. 40ECh. P.2 - Prob. 41ECh. P.2 - Prob. 42ECh. P.2 - Prob. 43ECh. P.2 - Prob. 44ECh. P.2 - Prob. 45ECh. P.2 - Prob. 46ECh. P.2 - Prob. 47ECh. P.2 - Prob. 48ECh. P.2 - Prob. 49ECh. P.2 - Prob. 50ECh. P.2 - Prob. 51ECh. P.2 - Prob. 52ECh. P.2 - Writing an Equation in General Form In Exercises...Ch. P.2 - Prob. 54ECh. P.2 - Writing an Equation in General Form In Exercises...Ch. P.2 - Prob. 56ECh. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Prob. 63ECh. P.2 - Prob. 64ECh. P.2 - Prob. 65ECh. P.2 - Prob. 66ECh. P.2 - Prob. 67ECh. P.2 - Analyzing a Line A line is represented by the...Ch. P.2 - Tangent Line Find an equation of the line tangent...Ch. P.2 - Prob. 70ECh. P.2 - Finding Points of Intersection Find the...Ch. P.2 - Prob. 72ECh. P.2 - Prob. 73ECh. P.2 - Prob. 74ECh. P.2 - Apartment Rental A real estate office manages an...Ch. P.2 - Prob. 76ECh. P.2 - Prob. 77ECh. P.2 - Prob. 78ECh. P.2 - Prob. 79ECh. P.2 - Prob. 80ECh. P.2 - Prob. 81ECh. P.2 - Prob. 82ECh. P.2 - Prob. 83ECh. P.2 - Prob. 84ECh. P.2 - Prob. 85ECh. P.2 - True or False? In Exercises 85 and 86, determine...Ch. P.3 - Writing Describe how a relation and a function are...Ch. P.3 - Prob. 2ECh. P.3 - Prob. 3ECh. P.3 - Prob. 4ECh. P.3 - Prob. 5ECh. P.3 - Prob. 6ECh. P.3 - Evaluating a Function In Exercises 5-12, evaluate...Ch. P.3 - Prob. 8ECh. P.3 - Prob. 9ECh. P.3 - Prob. 10ECh. P.3 - Prob. 11ECh. P.3 - Prob. 12ECh. P.3 - Prob. 13ECh. P.3 - Prob. 14ECh. P.3 - Prob. 15ECh. P.3 - Finding the Domain and Range of a Function In...Ch. P.3 - Prob. 17ECh. P.3 - Finding the Domain and Range of a Function In...Ch. P.3 - Finding the Domain and Range of a Function In...Ch. P.3 - Prob. 20ECh. P.3 - Prob. 21ECh. P.3 - Prob. 22ECh. P.3 - Prob. 23ECh. P.3 - Prob. 24ECh. P.3 - Prob. 25ECh. P.3 - Prob. 26ECh. P.3 - Prob. 27ECh. P.3 - Prob. 28ECh. P.3 - Prob. 29ECh. P.3 - Prob. 30ECh. P.3 - Prob. 31ECh. P.3 - Sketching a Graph of a Function In Exercises...Ch. P.3 - Prob. 33ECh. P.3 - Prob. 34ECh. P.3 - Prob. 35ECh. P.3 - Prob. 36ECh. P.3 - Prob. 37ECh. P.3 - Prob. 38ECh. P.3 - Prob. 39ECh. P.3 - Using the Vertical Line Test In Exercises 39-42,...Ch. P.3 - Prob. 41ECh. P.3 - Prob. 42ECh. P.3 - Prob. 43ECh. P.3 - Prob. 44ECh. P.3 - Prob. 45ECh. P.3 - Prob. 46ECh. P.3 - Prob. 47ECh. P.3 - Prob. 48ECh. P.3 - Prob. 49ECh. P.3 - Prob. 50ECh. P.3 - Prob. 51ECh. P.3 - Matching In Exercises 51-56, use the graph of...Ch. P.3 - Prob. 53ECh. P.3 - Prob. 54ECh. P.3 - Prob. 55ECh. P.3 - Prob. 56ECh. P.3 - Sketching Transformations Use the graph of f shown...Ch. P.3 - Sketching Transformations Use the graph of f shown...Ch. P.3 - Prob. 59ECh. P.3 - Prob. 60ECh. P.3 - Prob. 61ECh. P.3 - Prob. 62ECh. P.3 - Finding Composite Functions In Exercises 63-66,...Ch. P.3 - Prob. 64ECh. P.3 - Prob. 65ECh. P.3 - Prob. 66ECh. P.3 - Evaluating Composite Functions Use the graphs of f...Ch. P.3 - Ripples A pebble is dropped into a calm pond,...Ch. P.3 - Prob. 69ECh. P.3 - Prob. 70ECh. P.3 - Think About It In Exercises 71 and 72, find the...Ch. P.3 - Prob. 72ECh. P.3 - Ever, and Odd Functions The graphs of f, g, and h...Ch. P.3 - Prob. 74ECh. P.3 - Prob. 75ECh. P.3 - Prob. 76ECh. P.3 - Prob. 77ECh. P.3 - Prob. 78ECh. P.3 - Prob. 79ECh. P.3 - Prob. 80ECh. P.3 - Prob. 81ECh. P.3 - Prob. 82ECh. P.3 - Prob. 83ECh. P.3 - Prob. 84ECh. P.3 - Prob. 85ECh. P.3 - Prob. 86ECh. P.3 - Domain Find the value of c such that the domain of...Ch. P.3 - Domain Find all values of c such that the domain...Ch. P.3 - Prob. 89ECh. P.3 - Prob. 90ECh. P.3 - Prob. 91ECh. P.3 - Prob. 92ECh. P.3 - Graphical Reasoning An electronically controlled...Ch. P.3 - HOW DO YOU SEE IT? Water runs into a vase of...Ch. P.3 - Prob. 95ECh. P.3 - Prob. 96ECh. P.3 - Proof Prove that the function is odd...Ch. P.3 - Proof Prove that the function is even....Ch. P.3 - Prob. 99ECh. P.3 - Prob. 100ECh. P.3 - Length A right triangle is formed in the first...Ch. P.3 - Volume An open box of maximum volume is to be made...Ch. P.3 - Prob. 103ECh. P.3 - Prob. 104ECh. P.3 - Prob. 105ECh. P.3 - Prob. 106ECh. P.3 - Prob. 107ECh. P.3 - Prob. 108ECh. P.3 - Prob. 109ECh. P.3 - Prob. 110ECh. P.4 - Coterminal Angles Explain how to find coterminal...Ch. P.4 - Prob. 2ECh. P.4 - Prob. 3ECh. P.4 - Prob. 4ECh. P.4 - Prob. 5ECh. P.4 - Prob. 6ECh. P.4 - Prob. 7ECh. P.4 - Prob. 8ECh. P.4 - Prob. 9ECh. P.4 - Prob. 10ECh. P.4 - Prob. 11ECh. P.4 - Prob. 12ECh. P.4 - Prob. 13ECh. P.4 - Prob. 14ECh. P.4 - Prob. 15ECh. P.4 - Prob. 16ECh. P.4 - Evaluating Trigonometric Functions In Exercises...Ch. P.4 - Prob. 18ECh. P.4 - Prob. 19ECh. P.4 - Prob. 20ECh. P.4 - Prob. 21ECh. P.4 - Prob. 22ECh. P.4 - Prob. 23ECh. P.4 - Prob. 24ECh. P.4 - Prob. 25ECh. P.4 - Prob. 26ECh. P.4 - Prob. 27ECh. P.4 - Prob. 28ECh. P.4 - Prob. 29ECh. P.4 - Prob. 30ECh. P.4 - Prob. 31ECh. P.4 - Prob. 32ECh. P.4 - Prob. 33ECh. P.4 - Prob. 34ECh. P.4 - Prob. 35ECh. P.4 - Prob. 36ECh. P.4 - Prob. 37ECh. P.4 - Solving a Trigonometric Equation In Exercises...Ch. P.4 - Prob. 39ECh. P.4 - Prob. 40ECh. P.4 - Prob. 41ECh. P.4 - Prob. 42ECh. P.4 - Airplane Ascent An airplane leaves the runway...Ch. P.4 - Height of a Mountain While traveling across flat...Ch. P.4 - Prob. 45ECh. P.4 - Prob. 46ECh. P.4 - Prob. 47ECh. P.4 - Prob. 48ECh. P.4 - Prob. 49ECh. P.4 - Prob. 50ECh. P.4 - Prob. 51ECh. P.4 - Prob. 52ECh. P.4 - Prob. 53ECh. P.4 - Prob. 54ECh. P.4 - Prob. 55ECh. P.4 - Prob. 56ECh. P.4 - Prob. 57ECh. P.4 - Prob. 58ECh. P.4 - Prob. 59ECh. P.4 - Prob. 60ECh. P.4 - Prob. 61ECh. P.4 - Prob. 62ECh. P.4 - Prob. 63ECh. P.4 - Prob. 64ECh. P.4 - Prob. 65ECh. P.4 - Prob. 66ECh. P.4 - Prob. 67ECh. P.4 - Prob. 68ECh. P.4 - Prob. 69ECh. P.4 - EXPLORING CONCEPTS Restricted Domain Explain how...Ch. P.4 - Prob. 71ECh. P.4 - Prob. 72ECh. P.4 - Prob. 73ECh. P.4 - Prob. 74ECh. P.4 - Prob. 75ECh. P.4 - Prob. 76ECh. P.4 - Prob. 77ECh. P.4 - Prob. 78ECh. P.4 - Prob. 79ECh. P.4 - Prob. 80ECh. P - Finding Intercepts In Exercises 1-4, find any...Ch. P - Finding Intercepts In Exercises 1-4, find any...Ch. P - Finding Intercepts In Exercises 1-4, find any...Ch. P - Prob. 4RECh. P - Prob. 5RECh. P - Prob. 6RECh. P - Prob. 7RECh. P - Prob. 8RECh. P - Prob. 9RECh. P - Prob. 10RECh. P - Prob. 11RECh. P - Prob. 12RECh. P - Prob. 13RECh. P - Prob. 14RECh. P - Prob. 15RECh. P - Prob. 16RECh. P - Prob. 17RECh. P - Prob. 18RECh. P - Prob. 19RECh. P - Prob. 20RECh. P - Prob. 21RECh. P - Prob. 22RECh. P - Prob. 23RECh. P - Prob. 24RECh. P - Prob. 25RECh. P - Prob. 26RECh. P - Prob. 27RECh. P - Prob. 28RECh. P - Prob. 29RECh. P - Sketching a Line in the Plane In Exercises 27-30,...Ch. P - Prob. 31RECh. P - Prob. 32RECh. P - Finding Equations of Lines Find equations of the...Ch. P - Prob. 34RECh. P - Rate of Change The purchase price of a new machine...Ch. P - Break-Even Analysis A contractor purchases a piece...Ch. P - Prob. 37RECh. P - Prob. 38RECh. P - Evaluating a Function In Exercises 37-40, evaluate...Ch. P - Prob. 40RECh. P - Prob. 41RECh. P - Prob. 42RECh. P - Prob. 43RECh. P - Prob. 44RECh. P - Prob. 45RECh. P - Prob. 46RECh. P - Prob. 47RECh. P - Prob. 48RECh. P - Prob. 49RECh. P - Prob. 50RECh. P - Transformations of Functions Use a graphing...Ch. P - Think About It What is the minimum degree of the...Ch. P - Prob. 53RECh. P - Prob. 54RECh. P - Prob. 55RECh. P - Prob. 56RECh. P - Prob. 57RECh. P - Prob. 58RECh. P - Prob. 59RECh. P - Prob. 60RECh. P - Prob. 61RECh. P - Prob. 62RECh. P - Prob. 63RECh. P - Prob. 64RECh. P - Prob. 65RECh. P - Prob. 66RECh. P - Prob. 67RECh. P - Prob. 68RECh. P - Prob. 69RECh. P - Prob. 70RECh. P - Prob. 71RECh. P - Prob. 72RECh. P - Prob. 73RECh. P - Prob. 74RECh. P - Prob. 75RECh. P - Prob. 76RECh. P - Prob. 77RECh. P - Prob. 78RECh. P - Prob. 79RECh. P - Prob. 80RECh. P - Prob. 81RECh. P - Prob. 82RECh. P - Prob. 83RECh. P - Prob. 84RECh. P - Prob. 85RECh. P - Prob. 86RECh. P - Prob. 87RECh. P - Prob. 88RECh. P - Prob. 89RECh. P - Prob. 90RECh. P - Prob. 1PSCh. P - Finding Tangent Lines There are two tangent lines...Ch. P - Heaviside Function The Heaviside function H(x) is...Ch. P - Sketching Transformations Consider the graph of...Ch. P - Prob. 5PSCh. P - Prob. 6PSCh. P - Prob. 7PSCh. P - Prob. 8PSCh. P - Slope of a Tangent Line One of the fundamental...Ch. P - Slope of a Tangent Line Sketch the graph of the...Ch. P - Prob. 11PSCh. P - Graphing an Equation Explain how you would graph...Ch. P - Sound Intensity A large room contains two speakers...Ch. P - Sound Intensity Suppose the speakers in Exercise...Ch. P - Lemniscate Let d1 and d2 be the distances from the...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Evaluate the next integralarrow_forward1. For each of the following, find the critical numbers of f, the intervals on which f is increasing or decreasing, and the relative maximum and minimum values of f. (a) f(x) = x² - 2x²+3 (b) f(x) = (x+1)5-5x-2 (c) f(x) = x2 x-9 2. For each of the following, find the intervals on which f is concave upward or downward and the inflection points of f. (a) f(x) = x - 2x²+3 (b) g(x) = x³- x (c) f(x)=x-6x3 + x-8 3. Find the relative maximum and minimum values of the following functions by using the Second Derivative Test. (a) f(x)=1+3x² - 2x3 (b) g(x) = 2x3 + 3x² - 12x-4arrow_forwardFind the Soultion to the following dy differential equation using Fourier in transforms: = , хуо, ухо according to the terms: lim u(x,y) = 0 x18 lim 4x (x,y) = 0 x14 2 u (x, 0) = =\u(o,y) = -y لوarrow_forward
- Can you solve question 3,4,5 and 6 for this questionarrow_forwardwater at a rate of 2 m³/min. of the water height in this tank? 16) A box with a square base and an open top must have a volume of 256 cubic inches. Find the dimensions of the box that will minimize the amount of material used (the surface area). 17) A farmer wishes toarrow_forward#14 Sand pours from a chute and forms a conical pile whose height is always equal to its base diameter. The height o the pile increases at a rate of 5 feet/hour. Find the rate of change of the volume of the sand in the conical pile when the height of the pile is 4 feet.arrow_forward
- (d)(65in(x)-5 cos(x) dx mins by 5x-2x² 3x+1 dx -dx 20 Evaluate each the following indefinite integralsarrow_forward19 Evaluate each the following definite integrals: a) લ b) (+3) 6) (2-2)(+33) dxarrow_forward#11 If a snowball melts so its surface area decreases at a rate of 1cm²/min, find the rate at which the diameter decreases when the diameter is 6 cm.arrow_forward
- Use Deritivitve of the inverse to solve thisarrow_forwardEvaluate the following Limits: e6x-1 Lim +0Sin3x 7x-5x2 2x-1+ Cos 4x +6 c) Lim b) Lim + x³-x2 X-0 1-e' 4x d) Lim 6x²-3 X+0 6x+2x² Find the derivatives of the following functions using the Limit definition of derivativearrow_forward15A cylindrical tank with radius 8 m is being filled with water at a rate of 2 m³/min. What is the rate of change of the water height in this tank? 6)A box with a square base and an open top must box that will minimiarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY