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 Apr16 comment How do you show this property of a differentiable function given information about the derivative? @Thomas: It's not homework, but thanks for the hint anyway. If I integrate both sides of the above equation I get $f(-x) + C = -\int f(x)dx$ right? I am not sure what to do with that and in I general get thrown off by the constant whenever I try to use integration... Apr16 revised How do you show this property of a differentiable function given information about the derivative? edited title Apr16 asked How do you show this property of a differentiable function given information about the derivative? Apr10 accepted What is the best way to show that no positive powers of this matrix will be the identity matrix? Apr10 asked What is the best way to show that no positive powers of this matrix will be the identity matrix? Mar30 awarded Cleanup Mar30 revised Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$? rolled back to a previous revision Mar29 accepted Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$? Mar29 comment Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$? Thank you very much for this answer. Just one question: why is the first limit going to zero rather than infinity? Mar29 asked Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$? Mar13 accepted Proving elementary inverse image consequence Mar13 asked Proving elementary inverse image consequence Mar11 comment Is a linear tranformation onto or one-to-one? oh ok, so it wouldn't have been a function in the first place... Thanks for clearing that up for me! And thanks for another great answer of course! Mar11 comment Is a linear tranformation onto or one-to-one? Sorry if this is a stupid question, but is it always the case that whether a function is one-to-one depends only on the domain? For instance with the example $f(x) = x^2$ if the codomain were $0$, wouldn't the function still be one-to-one? Mar7 comment Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$ Thank you for the answer, although I must say that it isn't the same without the bold HINT formatting ;) Mar7 comment Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$ Definitely helps a lot, thank you! Mar7 accepted Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$ Mar7 comment Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$ thank you for the reply, I can understand much more now. Just to be absolutely clear: in order to determine which terms are added/deleted one could replace each $n$ in the original LHS with $n+1$, correct? Mar7 comment Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$ Unfortunately I still don't get it... with the induction, is it correct to sort of 'plug in' $n+1$ for each $n$? And somewhere in between $(2n+5)$ and $(4n-1)$ each term begins to be calculated differently? I can see why $2n+1$ is some odd number, but what is $4n-1$? Mar7 asked Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$