Flashcards
Continuity at a Point and Algebra of Continuous Functions
Flashcards do conjunto (8)
- 1Continuity at x0For all E>0 there exists d>0 st
|x-x0| |f(x)-f(x0)| - 2E-neighbourhood of y0Let E>0 and y0 in R
The set {y in R : |y-y0| - 3Triangle Inequality|a+b|<= |a| + |b|
- 4Reverse Triangle Inequality|a-b|>=||a|-|b||
- 5Algebra of Continuous Functions (1,2/4)If f,g : A->R are continuous at x0 in A then
* h(x)= f(x) +g(x)
*h(x)=f(x)g(x)
=> h is continuous at x0 - 6Algebra of Continuous functions (3/4)f:A->R cont at x0. g:B->R cont at f(x0), f(A) contained in B. Then
h(x) =g o f(x) =g(f(x))
=> h cont at x0 - 7Algebra of Continuous Functions (4/4)If f cont at x0 and f(x0)=/ 0
*1/f well defined function in a neighbourhood of x0
*1/f cont at x0 - 8—
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