Chapter 2.3- Continuity of Functions

Chapter 2.3- Continuity of Functions - ‣ Log ‣...

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Continuity Def: a function is continuous at point c if the limit as x approaches c of the function is equal to the function of c (Figure 2.3) Behavior = Location Types of Discontinuities Removable- it is ±xable Jump In±nite Oscillating Continuous Extension Hole in Graph- removable Continuous Function Figure 2.3
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Continuity A function f(x) is continuous on an interval [a,b] if f(x) is continuous for all values of c that are elements [a,b] F(x) is a continuous function if f(x) is continous for all values of c that are elements of the domain of f(x) Functions which are continuous or not Continuous Functions Polynomial Rational
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Unformatted text preview: ‣ Log ‣ Exponential ‣ Trigometric ‣ Non-continuous functions ◦ Piece-wise ‣ Greatest Integer ‣ If f and g are continuous at x=c, then f[g(x)] or g[f(x)] will be continuous at ◦ c. Intermediate Value Theorem for Functions ◦ Given f(x) is continuous on [a,b] and f(a) =< k=< f(b), there exists for c ‣ there exists [a,b] such that f(c) = k It says that if a function is ‣ continuous, it must hit all of the y-values between a and b Redefine f(x) Example 1 Must hit a value between those two points-f(x) is a continuous function-f(x) has an infinite discontinuity at x=0 F(x) is not continuous on...
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This note was uploaded on 02/26/2012 for the course MATHEMATIC 101 taught by Professor None during the Spring '12 term at Aurora University.

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Chapter 2.3- Continuity of Functions - ‣ Log ‣...

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