What is the difference between "differentiable" and "continuous"
Kind of off-topic but if infinitely differentiable implies differentiable which implies continuous that implies defined is there something stronger than infinitely differentiable?
real analysis - Why differentiability implies continuity, but ...
Why are all differentiable functions continuous, but not all continuous functions differentiable? For the same reason that all cats are animals, but not all animals are cats. Differentiability also …
functions - What is the definition of differentiability?
3 A function is differentiable (has a derivative) at point x if the following limit exists: $$ \lim_ {h\to 0} \frac {f (x+h)-f (x)} {h} $$ The first definition is equivalent to this one (because for this limit to …
The definition of continuously differentiable functions
Jan 24, 2015 · A function is said to be differentiable at a point if the limit which defines the derivate exists at that point. However, the function you get as an expression for the derivative …
Continuous differentiability implies Lipschitz continuity
In fact you can show that a differentiable function on an open interval (not necessarily a bounded interval) is Lipschitz continuous if and only if it has a bounded derivative. This is because any …
Continuous versus differentiable - Mathematics Stack Exchange
A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same c...
What does it mean for a function $f(x)$ to be differentiable at $x_0$?
Apr 28, 2017 · By definition, if x is a point in the domain of a function f, then f is said to be differentiable at x if the derivative f′ (x) exists. Intuitively, this means that the graph of f has a …
real analysis - Are Continuous Functions Always Differentiable ...
Oct 26, 2010 · So it would appear that if functions are not differentiable, it can only happen at a finite number of points. In real analysis, this concept of being differentiable everywhere except …
Is the complex function $f (z) = Re (z)$ differentiable?
May 18, 2016 · Since the conjugate function is the classical example of a non-complex-differentiable function (see for exampe this), it follows that the real part is not complex …
calculus - What is the basic difference between differentiable ...
What is the basic difference between differentiable, analytic and holomorphic function? Ask Question Asked 8 years, 8 months ago Modified 3 years, 8 months ago