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Section 1

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Definition of Continuity on an intreval

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Calculus Math

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Mar 1, 2020

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Section 1

(6 cards)

Definition of Continuity on an intreval

Front

f(x) is continuous on [a,b] if and only if f(x) is continuous at all points in [a,b]

Back

Squeeze Theorem

Front

If lim f(x) = lim g(x) = L than f(x) ≤ h(x) ≤ g(x) x→a x→a for all "x" in the neighborhood of "a"

Back

Definition of Continuity at a point

Front

f(x) is continuous at x=a if and only if f(a) and lim f(x) both exist and f(a) = lim f(x) x→a x→a

Back

Intermediate Value Theorem

Front

If f(x) is continuous on the closed interval on [a,b] and N is a number f(a) and f(b), then Ǝ (there exists) x=c in (a,b) such that f(c)=N

Back

definition of a limit

Front

if and only if L is the one number we can keep f(x) arbitrarily close to just by keeping "x" close enough to "a" but not equal to "a"

Back

f(x)=IxI

Front

IxI= {x if x is greater than or equal to 0} {-x if x less than 0 }

Back