What is the average value of a function $$f(x)$$ from $$a$$ to $$b$$ ?

The average value is given by $$\frac{1}{b-a} \times \text{integral from } a \text{ to } b f(x)dx$$ .

What is the integral of $$\frac{1}{x}$$ ?

$$\text{The integral is } \text{ln}|x| + C$$ .

How do you find the limit of a function as $$x$$ approaches a value?

Evaluate the function at that value or use algebraic manipulation to simplify.

What is the integral of $$\frac{2}{\text{sqrt}(1-x^2)}$$ ?

$$\text{The integral is } \text{asin}(x) + C$$ .

What is the definition of continuity at a point?

A function is continuous at a point if $$\text{lim}_{x \to c} f(x) = f(c)$$ .

What is the relationship between differentiation and integration?

Differentiation is the process of finding the rate of change, while integration is the process of finding the area under a curve.

AP Calculus AB Review #2

Flashcard

•

Mathematics

•

9th Grade - University

•

Practice Problem

•

Hard

•

CCSS

HSF-IF.C.7B

Standards-aligned

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15 questions

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FLASHCARD QUESTION

Front

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FLASHCARD QUESTION

Front

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FLASHCARD QUESTION

Front

What is the product rule for differentiation?

Back

FLASHCARD QUESTION

Front

What is the chain rule for differentiation?

Back

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

What is the Fundamental Theorem of Calculus?

Back

FLASHCARD QUESTION

Front

What is a piecewise function?

Back

A function defined by different expressions for different intervals of the domain.

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