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Level 514

Infinite Limits


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Continuous
is a quantitative variable that has a continuum of infinitely many possible values
Definition of Continuity
At a point:
Discontinuity
Not continuous at x=c
Existence of a Limit
Let f be a function and let c and L be real numbers. The limit of f(x) as x appoaches c is L if and only if lim f(x) = L
Continuity on a Closed Interval
A function f is continuous on the closed interval [a,b] if it is continuous on open interval (a,b) and lim f(x) = f(a)
Properties of Continuity
If b is a real number and f and g are continuous at x = c, then the following functions are also continuous at c.
Intermediate Value Theorem
If f(a) > 0 and f(b) < 0 then there is a real zero between a and b
vertical asymptote
comes from a factor in the denominator that doesnt cancel out
Properties of infinite Limits
Let c and L be real numbers and let f and g be functions such that