AB Calculus Exam Review #2

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What is a Riemann sum?

Back

A Riemann sum is a method for approximating the total area under a curve by dividing the region into small rectangles, calculating the area of each rectangle, and summing these areas.

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Front

What is the condition for a function to be concave up?

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A function is concave up on an interval if its second derivative is positive on that interval.

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How do you find the average value of a function over an interval?

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What does the notation @@ ext{lim}_{x ightarrow a}f(x)=L@@ mean?

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It means that as x approaches a, the function f(x) approaches the limit L.

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What is the relationship between the left Riemann sum, right Riemann sum, and the trapezoidal sum?

Back

The trapezoidal sum is generally a better approximation of the integral than either the left or right Riemann sums, especially for functions that are not linear.

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What is the significance of the derivative of a function?

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The derivative of a function represents the rate of change of the function with respect to its variable, indicating the slope of the tangent line at any point on the graph.

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What does it mean for a function to have a limit at a point?

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A function has a limit at a point if the values of the function approach a specific value as the input approaches that point.

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What is the difference between a definite integral and an indefinite integral?

Back

A definite integral computes the area under a curve between two specific points, while an indefinite integral represents a family of functions and includes a constant of integration.