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A function is continuous at a point x=c if the following three conditions are met...
the function hs to be defined when x=c, if there is no point, for example a hole, then it is discontinous
Equation Examples
Graph Examples
Notation
pwfx: {--,x<5
{--,x>5
-Jump: --o o-- , piece wise
-Hole: --o-- , rational function
- Vertical asymptote: line go up , rational function
if theres no eqaul sign on the inequalities , the fx is not defined
Rational fx the denotminator is o numerator doesn't matter
function defined f(c) is defined
f(a) is defined
If the limit of f(x) as x approaches c is the same from both the right and the left, then we say that the limit of f(x) as x approaches c is L.
Equation Examples
Graph Examples
Notation
-Example where the limit doesnt exist jump asymptote
- Piece wise function(PWF): looking for the 2 pieces don't equal each other at that point
-Rational function: #/0
limit exists, lim f(x) = lim f(c)
lim f(x) exist
X --- a
the limit at f(x) and c must be equal at the same y value
Equation Examples
Graph Examples
Notation
-We're looking for a hole with a dot underneath
-Rational function with 0/0
-Dot piece wise function
f(c) = lim f(x)
x-> c
lim f(x) = f(a)
X --> a