- published: 15 Jan 2014
- views: 79046
In differential calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. The rate of change is usually with respect to time. Because science and engineering often relate quantities to each other, the methods of related rates have broad applications in these fields. Because problems involve several variables, differentiation with respect to time or one of the other variables requires application of the chain rule.
Fundamentally, if a function is defined such that , then the derivative of the function can be taken with respect to another variable. (The Variable is frequently used as many Related Rates problems apply to finding changes with respect to time.) We assume is a function of , i.e. . Then , so
Written in Liebnitz notation, this is:
The value of this is: if it is know how changes with respect to , then we can determine how changes with respect to and vice versa. We can extend this application of the chain rule with the sum, difference, product and quotient rules of calculus, etc.
Rate may refer to:
Related is an American comedy-drama series that aired on The WB network during the 2005-2006 television season. It revolved around the lives of four close-knit sisters - of Italian descent, raised in Brooklyn - living in New York City.
The show was created by former Sex and the City writer Liz Tuccillo, and executive produced by Friends co-creator Marta Kauffman. Despite heavy promotion, initial ratings did not warrant the show being picked up for a second season when The WB network was folded into The CW.
The untitled Related theme song is sung by The Veronicas, whose music was regularly featured in episodes.
Calculus 1 Lecture 2.8 Part 4: Applications with Related Rates
Calculus 1 Lecture 2.8 Part 3: Applications with Related Rates
Calculus 1 Lecture 2.8 Part 1: Applications with Related Rates
Calculus 1 Lecture 2.8 Part 2: Applications with Related Rates
I work through multiple examples of Related Rate problems from Calculus. In the first example I keep saying speed instead of velocity and I say that speed can be negative. Since speed is the absolute value of velocity this is incorrect. Annotations have been included, but these are not visible without Flash. Related Rates Part 2 Linear vs Angular Speed https://www.youtube.com/watch?v=JBHQYQSdmJQ&index;=38&list;=PL67C119EDA6BDE946 Calculus Related Rates Example Volume of Cone https://www.youtube.com/watch?v=FoB4qIKQxZ0 Check out http://www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com
Related Rates: Easy how to process with a boat being pulled into shore by a winch. 7 more related rates examples at https://calcworkshop.com: 1. Air being pumped into a balloon 2. Conical tanks 3. Ladder sliding down a wall 4. Pebble dropped in pond 5. Edges of cube expanding 6. Radar tracking station and airplane flight path 7. Cone at sand and gravel pit For more lessons covering all topics in Calculus I and Calculus II, visit https://calcworkshop.com For our online-calculus course: https://calcworkshop.com/online-calculus-course/
Visit my website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding. In this video we take a look at related rates problems!
Calculus 1 Lecture 2.8 Part 4: Applications with Related Rates
Calculus 1 Lecture 2.8 Part 3: Applications with Related Rates
Calculus 1 Lecture 2.8 Part 1: Applications with Related Rates
Calculus 1 Lecture 2.8 Part 2: Applications with Related Rates
I work through multiple examples of Related Rate problems from Calculus. In the first example I keep saying speed instead of velocity and I say that speed can be negative. Since speed is the absolute value of velocity this is incorrect. Annotations have been included, but these are not visible without Flash. Related Rates Part 2 Linear vs Angular Speed https://www.youtube.com/watch?v=JBHQYQSdmJQ&index;=38&list;=PL67C119EDA6BDE946 Calculus Related Rates Example Volume of Cone https://www.youtube.com/watch?v=FoB4qIKQxZ0 Check out http://www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com
Related Rates: Easy how to process with a boat being pulled into shore by a winch. 7 more related rates examples at https://calcworkshop.com: 1. Air being pumped into a balloon 2. Conical tanks 3. Ladder sliding down a wall 4. Pebble dropped in pond 5. Edges of cube expanding 6. Radar tracking station and airplane flight path 7. Cone at sand and gravel pit For more lessons covering all topics in Calculus I and Calculus II, visit https://calcworkshop.com For our online-calculus course: https://calcworkshop.com/online-calculus-course/
Visit my website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding. In this video we take a look at related rates problems!
The power of angels
You left at my door
I wrapped it up
In tinfoil
And hastened away
Towards hills
Begging for someone
to give me a sign
But my heart wrapped in silver
Could cry any louder
Hello, the silver hearts
That you cannot remark
Go on, go on
You shall never know
You shall ever be