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  2. AP Calculus
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What is the Pythagorean Theorem?

a2+b2=c2a^2 + b^2 = c^2a2+b2=c2

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What is the Pythagorean Theorem?

a2+b2=c2a^2 + b^2 = c^2a2+b2=c2

Area of a rectangle?

A=lcdotwA = l cdot wA=lcdotw

Explain the chain rule in the context of related rates.

When differentiating implicitly with respect to time, the chain rule is used to find the derivative of variables that are functions of time. For example, ddtx2=2xdxdt\frac{d}{dt}x^2 = 2x \frac{dx}{dt}dtd​x2=2xdtdx​.

Why is drawing a diagram helpful in related rates problems?

Visualizing the problem helps to understand the relationships between variables and how they change with respect to each other.

Why is it important to identify constants before differentiating?

Constants can be directly substituted into the equation before differentiation, simplifying the process. The derivative of a constant is zero.

Steps to solve related rates problems?

  1. Read carefully & identify key values. 2. Draw a diagram. 3. Set up an equation. 4. Implicit differentiation. 5. Substitute known values. 6. Solve for the desired rate.

First step when solving related rates?

Read the problem carefully and identify significant values. Circle, underline, or rewrite these values.

What to do after setting up the equation?

Differentiate the equation implicitly with respect to time (t), applying the chain rule.

What's the last step in related rates?

Solve for the desired rate, ensuring units match the expected units.