GR9768 Q-64
Posted: Tue Nov 01, 2011 4:11 pm
can anyone tell me the solution with full explanation
Suppose f is a continuous real-valued function defined on the closed interval [0,1]. Which of the following must be true?
1. There is a constant C>0 such that |f(x)-f(y)|<= C for all x and y in [0,1]
2. There is a constant D>0 such that |f(x)-f(y)|<= 1 for all x and y in [0,1] that satisfy |x-y|<=D
3. There is a constant E>0 such that |f(x)-f(y)|<= E|x-y| for all x and y in [0,1]
plz reply
Suppose f is a continuous real-valued function defined on the closed interval [0,1]. Which of the following must be true?
1. There is a constant C>0 such that |f(x)-f(y)|<= C for all x and y in [0,1]
2. There is a constant D>0 such that |f(x)-f(y)|<= 1 for all x and y in [0,1] that satisfy |x-y|<=D
3. There is a constant E>0 such that |f(x)-f(y)|<= E|x-y| for all x and y in [0,1]
plz reply