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Jun
27
comment Continuity of $f^{(n-1)}$ in Taylor's Theorem with Mean-value remainder
@DanielFischer I'm probably tired, but how can you do the first step?
Jun
27
comment Continuity of $f^{(n-1)}$ in Taylor's Theorem with Mean-value remainder
@DanielFischer I think that you always start the proof with $n=1$ (applied to $g$). Then you focus on a smaller interval, but how do you choose $x-1$ if the MVT is not applicable to $g$ on the whole $[\alpha,\beta]$?
Jun
27
comment Continuity of $f^{(n-1)}$ in Taylor's Theorem with Mean-value remainder
@Wakaka But the MVT for $g$ is the MVT. How can you start the proof if the assumptions of the MVT are violated?
Jun
27
comment If a function is enclosed by lower and upper sums, does its limit w.r.t. partitions equals the integral
Please, do not use $f$ for two really distinct things!
Jun
27
comment Continuity of $f^{(n-1)}$ in Taylor's Theorem with Mean-value remainder
So you can prove the Mean Value Theorem without assuming that $f$ is continuous on $[a,b]$. Can you show us a complete proof?
Jun
27
revised $\|f(x)-f(y)\|\ge c\|x-y\|$ for all $x,y\in U, c>0$-> continuously differentiable inverse function $g:f(U)\to U$
added 27 characters in body
Jun
27
comment Can we find an example?
So you wrote a theorem and you ar asking us if we can find any application?
Jun
27
comment Can we find an example?
It looks like an excerpt from some book. Can you find anything in the references?
Jun
27
revised Injectivity of the Differential of Smooth Map
added 120 characters in body
Jun
26
comment The image of the inverse of a continuous function
A point is in the closure if and only if it is the limit of a sequence of points from the set.
Jun
26
answered Find inverse $f^{-1}$ of a function $f(x,y)=(x-y,x-10y)$
Jun
26
comment The image of the inverse of a continuous function
Read: $f(x)=c$.
Jun
26
answered The image of the inverse of a continuous function
Jun
26
revised Equivalent formulations: pure contraction
edited body
Jun
25
answered Prove that the reciprocal of a polynomial function $f(x)$ is uniformly continuous on $R$.
Jun
25
reviewed Approve Sum of real answers to $\frac{x^2+4x+1}{x}+\frac{3x}{x^2+4x+1}=4$
Jun
25
awarded  analysis
Jun
24
reviewed Close A question on vector subspace
Jun
24
revised How to compute the integral $ I\left(c\right)=\int_{0}^{1}{\frac{\ln(1-cx)}{1+x}dx} $
added 15 characters in body
Jun
23
revised How to compute the derivative of $ (f^{-1})'(a) $ for some $a?$
added 1 character in body