Limits
Limits describe the value that a function approaches as its input gets closer to a particular point.

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Differentiation
Differentiation is the process of finding the derivative of a function. It measures how a quantity changes with respect to changes in another variable, typically representing instantaneous rate of change or slope.

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Derivatives of Trigonometric and Logarithmic Functions
These derivatives follow specific rules (e.g., derivative of sin(x) is cos(x), derivative of ln(x) is 1/x). Mastering these rules is essential for analyzing functions involving trigonometric or logarithmic expressions.

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Curve-Sketching
Curve-sketching uses derivatives and other function properties to understand a graph’s behavior. This includes identifying intercepts, increasing/decreasing intervals, concavity, asymptotes, and critical points to produce an accurate sketch of the function.

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Anti-Derivatives
An anti-derivative is a function whose derivative gives the original function. It represents the reverse process of differentiation and forms the basis of integration.

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Integration
Integration computes the accumulated total of a quantity, such as area under a curve. It includes both indefinite integrals (general antiderivatives) and definite integrals (numerical accumulation over an interval).

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Maximum/Minimum Problems
These problems use derivatives to identify points where a function reaches its highest or lowest value. They are essential in optimization tasks across mathematics and applications.

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Rate Problems
Rate problems, often involving related rates, use derivatives to describe how one changing quantity affects another. They model real-time changes such as motion, fluid flow, or geometric growth.

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Growth/Decay Problems
Growth and decay problems use differential equations to model processes that increase or decrease over time, such as population growth or radioactive decay. Solutions often involve exponential functions.