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Calculus

Calculus

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Statement 4 (horizontal asymptote)

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Last updated

6 years ago

Date created

Mar 1, 2020

Cards (5)

Section 1

(5 cards)

Statement 4 (horizontal asymptote)

Front

The horizontal line y = b is a horizontal asymptote of the graph of the function f if at least one of lim f(x) x−→∞ and lim f(x) x−→−∞ is the number b.

Back

Extreme Value Theorem

Front

If a function f is continuous on a closed interval [a, b], then f has an absolute maximum value and an absolute minimum value on [a, b].

Back

Statement 1 (Critical Number)

Front

A critical number (or critical point) of a function f is any number c in the domain of f such that f′(c) = 0 or f′(c) does not exist.

Back

Statement 2 (point of inflection)

Front

A point (a,f(a)) on the graph of f at which the concavity of the graph changes is a point of inflection.

Back

Statement 3 (vertical asymptote)

Front

The vertical line x = a is a vertical asymptote of the graph of the function f provided that at least one of the one-sided limits lim f(x) as x approaches a from the right and lim f(x) as c approaches a from the left is ∞ or −∞.

Back