Calculus Basics

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What is a one-sided limit?

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A one-sided limit is the value that a function approaches as the input approaches a specified point from one side (either from the left or the right).

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What is a two-sided limit?

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A two-sided limit is the value that a function approaches as the input approaches a specified point from both sides.

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What are the properties and rules for evaluating limits?

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Properties and rules for evaluating limits include limit laws such as the sum, difference, product, and quotient rules, as well as the squeeze theorem and L'Hôpital's rule.

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What is the average rate of change?

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The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

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What is the difference quotient?

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The difference quotient is a formula that provides the average rate of change of a function over a small interval, and is used to define the derivative. It is given by (f(x+h) - f(x)) / h.

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What is the definition of the derivative?

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The derivative of a function at a point is the limit of the difference quotient as the interval approaches zero. It represents the instantaneous rate of change of the function at that point.

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What is the definition of tangent lines?

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A tangent line to a curve at a given point is a straight line that just touches the curve at that point and has the same slope as the curve at that point.

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What is the definition of normal lines?

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A normal line to a curve at a given point is a straight line perpendicular to the tangent line at that point.

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Tangent line (Equation)

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Normal line (Equation)

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