Calculus Review (limits, continuity, derivatives, integration)

Front

What is a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches some value. It is fundamental in defining derivatives and integrals.

Front

Define continuity in a function.

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A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point.

Tags

CCSS.HSF.IF.A.2

Front

What is the derivative of a function?

Back

The derivative of a function represents the rate of change of the function with respect to its variable. It is the slope of the tangent line to the function's graph.

Front

How do you find the derivative using implicit differentiation?

Back

To find the derivative using implicit differentiation, differentiate both sides of the equation with respect to x, treating y as a function of x, and then solve for dy/dx.

Front

What is the integral of a function?

Back

An integral represents the area under the curve of a function over a specified interval. It is the reverse process of differentiation.

Front

What is the Fundamental Theorem of Calculus?

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Front

What does it mean for a function to have an absolute maximum?

Back

A function has an absolute maximum at a point if the function's value at that point is greater than or equal to the values of the function at all other points in its domain.

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How do you determine critical points of a function?

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Critical points occur where the derivative is zero or undefined. These points are potential locations for local maxima, minima, or points of inflection.

Front

What is the power rule for differentiation?

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Front

What is the product rule for differentiation?

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