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AP Calculus AB Limits and Continuity

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Section 1

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Limit from the left

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Calculus Math

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Mar 1, 2020

Cards (20)

Section 1

(20 cards)

Limit from the left

Front

lim x → a⁻

Back

Limit of a Constant Property

Front

lim x → a of c = c

Back

Definition of Continuity for Piecewise Functions

Front

lim x → a⁻ of f(x) = lim x → a⁺ of f(x)

Back

Limit of a Sum Property

Front

lim x → a of [f(x) + g(x)] = lim x → a of f(x) + lim x → a of g(x)

Back

Limit of a Root Property

Front

lim x → a of ⁿ√[f(x)] = ⁿ√[lim x → a of f(x)], if the root on the right side exists

Back

Limit of (1 - cos x)/x

Front

(1 - cos x)/x → 0

Back

Limit at a Hole

Front

f(c) is not defined, but lim x → c of f(x) exists

Back

Limit at a Break

Front

f(c) is defined, but lim x → c of f(x) doesn't exist

Back

Limit of sin x/x

Front

sin x/x → 1

Back

Intermediate Value Theorem

Front

If f is continuous on the closed interval [a, b], then there is at least one number, c, on the interval of [a, b] such that f(a) < f(c) < f(b)

Back

Limit of a Product Property

Front

lim x → a of f(x) / g(x) = (lim x → a of f(x)) / (lim x → a of g(x))

Back

Limit of a Difference Property

Front

lim x → a of [f(x) - g(x)] = lim x → a of f(x) - lim x → a of g(x)

Back

Limit of x Property

Front

lim x → a of x = a

Back

Limit from the right

Front

lim x → a⁺

Back

Limit at a Point Discontinuity

Front

f(c) is defined, and lim x → c of f(x) exists, f(c) != lim x → c of f(x)

Back

Limit of a Constant Multiple Property

Front

lim x → a of [c f(x)] = c lim x → a of f(x)

Back

Definition of Continuity

Front

A function is continuous at x = c if 1: f(c) is defined 2: lim x → c of f(x) exists 3: lim x → c of f(x) = f(c)

Back

Limit of (1 - cos x)/x^2

Front

(1 - cos x)/x² → 1/2

Back

Limit of a Power Property

Front

lim x → a of [f(x)]ⁿ = [lim x → a of f(x)]ⁿ, where n is a rational number

Back

BOBO BOTN EATS DC

Front

BOBO: Bigger On Bottom, y = 0 BOTN: Bigger On Top, None EATS DC: Exponents Are The Same, Divide Coefficients

Back