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2h
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
3h
comment Limit of $\frac{f\left(x+g\left(x\right)\right)-f\left(g\left(x\right)\right)}{x}$ as $x\to 0$
oopse, fixed...
3h
comment Using the same limit for a second derivative
hmm I understand. Is there a similar proof without L'Hopital? As we haven't learned it yet I'm not sure I can use it.. Thanks anyway :)
May
18
comment Finding the limit at $a$ of $\left(\frac{f\left(x\right)} {f\left(a\right)}\right)^{\frac{1}{g\left(x\right)}}$
$\ln x $ is differentiable at $x\neq 0$ and $f(x) $ differentiable at $x$ so by the chain rule it's differentiable there? And this actually makes a lot of sense, though I'm not sure how I could think of something like that myself
May
12
comment Proving the Takagi function is lipschitz for $c\cdot d<1$
Took me a day buy I got it. Thanks
May
5
comment One-one and continuous $\implies$ strictly monotonic
I think you mean contradicts injectivity, Edit: well you were faster than me :P
May
5
comment Proving that a union of a countable and an uncountable set is equivalent to the uncountable set (proof check)
@tetori This is the next topic so I guess I'll realize it soon :P
May
4
comment Analysis: Basic Sequence Proof
Didn't downvote myself, but I think it's getting downvoted because it answers the half of what he asks that is "hidden" at the end.
May
4
comment Analysis: Basic Sequence Proof
Yep, you got it.
Apr
28
comment Show that the series is absolutely convergent
Is showing that the series of absolute values converges enough to conclude that the original series converges absolutely, or do you have to show that the original series converges as well?
Apr
23
comment Does Russel's paradox preclude us from using the power set to generate every possible set?
Well as far as I understand, "the set of all things" is not a set, you can't just say "I take everything and call it $A$", and there is actually quite a delicate process describing what is or isn't a set.
Apr
23
comment Fixed point of a differentiable function on a closed interval
@cantorhead, oh well that makes it easy. Thanks!
Apr
23
comment Fixed point of a differentiable function on a closed interval
@GitGud Oh oops, fixed
Apr
14
comment Finding a counter example for $ \left(A+A\right)'\subseteq\left(A'+A\right)\cup\left(A'+A'\right)$
I thought about the idea of searching for a set $A$ with no limit points, such that $A+A$ will have a limit point, but wasn't able to figure one out myself. Even the solution you gave took me quite a while to understand, but I get it now. Thanks!
Apr
3
comment Why can you place in the recursive definition to find the limit?
That makes everything clear. Thank you very much!
Apr
1
comment Finding the limit of $\sqrt[n]{{kn \choose n}}$
Got it! Thanks!
Apr
1
comment Finding the limit of $\sqrt[n]{{kn \choose n}}$
Not quite sure about how you simplified the last step, will try it by hand and come back :P
Apr
1
comment Finding the limit of $\sqrt[n]{{kn \choose n}}$
unfortunately I am unable to follow most of proof 1, and in proof 2 I'm not sure how the lemma gives that $\lim \frac{(kn)!^{1/n}}{(kn)^k} = e^{-k}$, or how you did the algebra...
Mar
23
comment Finding $\sup$ of $\{\sqrt{n} - \lfloor\sqrt{n}\rfloor | n\in\mathbb{N}\}$
hmm I understand that, still not sure how to use it though :P
Mar
23
comment Finding $\sup$ of $\{\sqrt{n} - \lfloor\sqrt{n}\rfloor | n\in\mathbb{N}\}$
Well that's a really nice way of doing it. Didn't think about breaking the number into easier to manage numbers ><