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Jun
7
comment Proving the inequality $2^{-1+\frac{1}{n}}\left(x+1\right)\leq\left(x^{n}+1\right)^{\frac{1}{n}}$ for $n\in\mathbb{N} $ and $x>0$
Well that does it...
Jun
7
comment Proving the inequality $2^{-1+\frac{1}{n}}\left(x+1\right)\leq\left(x^{n}+1\right)^{\frac{1}{n}}$ for $n\in\mathbb{N} $ and $x>0$
We haven't really talked about properties of convex function, so I have no idea how to justify what you wrote, any other options?
Jun
7
comment Proving the inequality $2^{-1+\frac{1}{n}}\left(x+1\right)\leq\left(x^{n}+1\right)^{\frac{1}{n}}$ for $n\in\mathbb{N} $ and $x>0$
I tried using Binomial Theorem, It's how I solved the other side of the inequality, but with this side I had pretty much the same thing as with Taylor polinomial, which I had no idea how to proceed with
Jun
7
comment Proving the inequality $2^{-1+\frac{1}{n}}\left(x+1\right)\leq\left(x^{n}+1\right)^{\frac{1}{n}}$ for $n\in\mathbb{N} $ and $x>0$
@Stromael, fixed, thanks...
Jun
7
revised Proving the inequality $2^{-1+\frac{1}{n}}\left(x+1\right)\leq\left(x^{n}+1\right)^{\frac{1}{n}}$ for $n\in\mathbb{N} $ and $x>0$
edited body
Jun
7
asked Proving the inequality $2^{-1+\frac{1}{n}}\left(x+1\right)\leq\left(x^{n}+1\right)^{\frac{1}{n}}$ for $n\in\mathbb{N} $ and $x>0$
Jun
6
comment Proving the ranges of repeated iteration of a one-to-one function from $X$ to a subset are disjoint
That is simple enough, thanks!
Jun
6
accepted Proving the ranges of repeated iteration of a one-to-one function from $X$ to a subset are disjoint
Jun
6
asked Proving the ranges of repeated iteration of a one-to-one function from $X$ to a subset are disjoint
Jun
5
comment Determinant of matrix with trigonometric functions
Well that makes sense, I failed to see it split like that myself ><". Thank you
Jun
5
accepted Determinant of matrix with trigonometric functions
Jun
5
comment Determinant of matrix with trigonometric functions
@Mann I didn't get it honestly :/ Still thinking about it, I do see that there seems to be a pattern of matrix multiplication after expanding to $\cos(a_i)\cos(b_j)+\sin(a_i)\sin(b_j)$ but wasn't able to take it any further than that...
Jun
5
comment Determinant of matrix with trigonometric functions
@NeilRoy I did that myself as well :P Unfortunately it didn't help me too much...
Jun
5
asked Determinant of matrix with trigonometric functions
May
26
comment find the rank of a linear mapping such that $T^2=0$
Since you need just one correct answer, what happens if $T\equiv0$?
May
26
comment Limit of $\frac{f\left(x+g\left(x\right)\right)-f\left(g\left(x\right)\right)}{x}$ as $x\to 0$
I see.. Thank you!
May
26
accepted Limit of $\frac{f\left(x+g\left(x\right)\right)-f\left(g\left(x\right)\right)}{x}$ as $x\to 0$
May
25
accepted Using the same limit for a second derivative
May
25
comment Limit of $\frac{f\left(x+g\left(x\right)\right)-f\left(g\left(x\right)\right)}{x}$ as $x\to 0$
Oh wow... looks like I'm already too tried.. Thank you very much
May
25
revised Limit of $\frac{f\left(x+g\left(x\right)\right)-f\left(g\left(x\right)\right)}{x}$ as $x\to 0$
edited title