Slide 2.7.pptx - Related Rates What are the Related Rates...

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Related Rates
What are the Related Rates? Suppose that two variables x and y are functions of a variable, t: Then and are the rates of change of x and y with respect to t.
Sometimes x and y are related by means of an equation, such as: Differentiate implicitly with respect to t: The derivatives are called related rates since they’re related by means of an equation. We can find if is given and vice versa.
Example 1 How fast does the radius of a spherical soap bubble change at the moment when the radius is 1 cm if the air is blown into it at the rate of 10 cm 3 /sec? How to solve problems of this kind? You should follow the 7 steps as below:
1. Draw diagram (if needed) 2. Write down what is given and what is asked for 3. Write the equation that relates the variables 4. Implicitly differentiate 5. Plug in given values 6. Find values that are not directly given and plug them in as well (if needed) 7. Find the unknown V sphere = 4/3 pi R 3 1 dV/dt = 4 pi R 2 dR/dt Given:
Example 2 How fast does the water level drop when a cylindrical tank with a radius of 1 m is