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36 Cards in this Set
- Front
- Back
slope of the secant line
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The limit of (f):
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common types of behavior associated with Nonexisitance of a Limit:
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1. f(x) approaches a different number form the right side of c than it approaches from the left side
2. f(x) increases or decreases without bound as x approaches c. 3. f(x) oscillates between two fixed values as x approaches c. |
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Definition of Limit:
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b
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c
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bL
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LK
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If p is a polynomial function and c is a real number, then
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p(c)
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If r is a rational function given by r(x) = p(x)/q(x) and c is a real number such that a(c) can not equal 0, then
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Let n be a positive integer. The following limit is valid for all c if n is odd, and is valid for c>0 if n is even.
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If f and g are functions such that the limit of g(x)= L as x approaches c and the limit of f(x) = f(L) as x approaches L, then
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sin c
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cos c
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tan c
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sec c
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csc c
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functions that agree at all but one point
let c be a real number and let f(x) = g(x) for all x can not equal c in an open interval containing c. if the limit of g(x) as x approaches c exists, then the limit of c(x) also exisist and |
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strategy for finding limits
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The squeeze theorem
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1
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0
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Definition of Continuity
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The Existence of a limit
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let f be a function and let c and L be real numbers. The limit of f(x) as x approaches c is L if and only if
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Definition of Continuity on a closed interval
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The Properties of Continuity
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if b is a real number aned f and g are continuous at x=c, then the following functions are also continouous at c.
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Continuity of a Composite function
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The Intermediate Value Theorem
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If f is continuous on the colsed interval [a,b] and k is any number between f(a) and f(b), then there is at least one number c in [a,b] such that f(c) = k
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Definition of Infinite Limits
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Definition of Vertical Asymptote:
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If f(x) approaches infinity (or negative infinity) as x approaches c from the right or the left, then the line x = c is a vertical asymptote of the graph of f.
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Vertical asymptotes:
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let f and g be continuous on an open interval containing c. If f(c) does not equal 0, g(c) does not equal 0, and there exists an open interval containing c such that g(x) does not equal 0 for all x does not equal c in the interval, then the graph of the function given by
h(x) = f(x) / g(x) has a vertical asymptote at x = c |
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Properties of Infinite Limits
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