Calculus AB Final Review (Semester 1)

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What is the definition of continuity in a function?

Back

A function f(x) is continuous at a point x = a if the following three conditions are met: 1) f(a) is defined, 2) the limit of f(x) as x approaches a exists, and 3) the limit equals f(a).

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What is a removable discontinuity?

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A removable discontinuity occurs at a point where a function is not defined, but can be made continuous by defining or redefining the function at that point.

Tags

CCSS.HSF-IF.C.7B

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What is a non-removable discontinuity?

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A non-removable discontinuity occurs at a point where the function cannot be made continuous by any means, typically due to a vertical asymptote.

Tags

CCSS.HSF-IF.C.7D

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What does a negative first derivative indicate about a function?

Back

If a function has a first derivative that is negative, it indicates that the function is decreasing.

Tags

CCSS.HSF.IF.B.4

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What is the derivative of a constant function?

Back

The derivative of a constant function is zero.

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How do you find the derivative of a polynomial function?

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To find the derivative of a polynomial function, apply the power rule: if f(x) = ax^n, then f'(x) = n * ax^(n-1).

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What is the power rule for differentiation?

Back

The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).

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What is the product rule for differentiation?

Back

The product rule states that if u(x) and v(x) are functions, then the derivative of their product is given by (uv)' = u'v + uv'.

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What is the quotient rule for differentiation?

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The quotient rule states that if u(x) and v(x) are functions, then the derivative of their quotient is given by (u/v)' = (u'v - uv')/v^2.

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What is the chain rule for differentiation?

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The chain rule states that if a function y = f(g(x)), then the derivative is given by dy/dx = f'(g(x)) * g'(x).