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To solve a related rates problem, first draw a picture that illustrates the relationship between the two or more related quantities that are changing with respect to time. In terms of the quantities, state the information given and the rate to be found. Find an equation relating the quantities.
Nov 16, 2022 · In related rates problems we are give the rate of change of one quantity in a problem and asked to determine the rate of one (or more) quantities in the problem. This is often one of the more difficult sections for students.
If two related quantities are changing over time, the rates at which the quantities change are related. For example, if a balloon is being filled with air, both the radius of the balloon and the volume of the balloon are increasing.
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.
Feb 22, 2021 · Calculate the Speed of an Airplane. How To Solve Related Rates Problems. We use the principles of problem-solving when solving related rates. The steps are as follows: Read the problem carefully and write down all the given information. Sketch and label a graph or diagram, if applicable.
Related Rates. Learning Objectives. Express changing quantities in terms of derivatives. Find relationships among the derivatives in a given problem. Use the chain rule to find the rate of change of one quantity that depends on the rate of change of other quantities.
Join us as we explore the intriguing relationship between the rate at which a circle's radius expands and the corresponding rate of area growth. Using the tools of calculus, specifically derivatives, we'll tackle this concept, providing a practical application to real-world problems involving rates of change.
- 8 min
- Sal Khan
