How about f(x) = floor(x)? (On, say, [0,1].) It's monotone and therefore of bounded variation, but is not Lipschitz continuous (or even continuous).
A circle
a circle
NO
The answer is yes is and only if da limit of the sequence is a bounded function.The suficiency derives directly from the definition of the uniform convergence. The necesity follows from making n tend to infinity in |fn(x)|
If the range is the real numbers, it has a lower bound (zero) but no upper bound.
No. y = 1/x is continuous but unbounded.
That depends! The identity operator must map something from a space X to a space Y. This mapping might be continuous - which is the case if the identify operator is bounded - or discontinuous - if the identity operator is unbounded.
A signal is bounded if there is a finite value such that the signal magnitude never exceeds , that is for discrete-time signals, or for continuous-time signal (Source:Wikipedia)
A circle
a circle
NO
GREEN'S THEOREM: if m=m(x,y) and n= n(x,y) are the continuous functions and also partial differential in a region 'r' of x,y plane bounded by a simple closed curve c. DIVERGENCE THEOREM: if f is a vector point function having continuous first order partial derivatives in the region v bounded by a closed curve s
What is the area bounded by the graph of the function f(x)=1-e^-x over the interval [-1, 2]?
A function whose upper bound would have attained its upper limit at a bound. For example, f(x) = x - a whose domain is a < x < b The upper bound is upper bound is b - a but, because x < b, the bound is never actually attained.
The answer is yes is and only if da limit of the sequence is a bounded function.The suficiency derives directly from the definition of the uniform convergence. The necesity follows from making n tend to infinity in |fn(x)|
A function may have a finite number of discontinuities and still be integrable according to Riemann (i.e., the Riemann integral exists); it may even have a countable infinite number of discontinuities and still be integrable according to Lebesgue. Any function with a finite amount of discontinuities (that satisfies other requirements, such as being bounded) can serve as an example; an example of a specific function would be the function defined as: f(x) = 1, for x < 10 f(x) = 2, otherwise
the abdominal what? ... the abdomen is that part of the human body inferiorly continuous with the pelvic area, and bounded superiorly by the diaphragm.