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Answer by Iuli for Compute $\lim_{x\to0} \frac{\cosh x\cosh 2x\cosh 3x \cdots...
I should want to leave my answer in comment box but my partial answer is too long. I try the following , I know there are a lot of calculations but I think what I've done can help us to find out the...
View ArticleAnswer by Ralph Tandetzky for Compute $\lim_{x\to0} \frac{\cosh x\cosh...
By Taylor's theorem we have $\cosh x = 1 + \frac{x^2}2 + O(x^4)$. So ignoring the parts in the product which tend to $0$ faster than $x^2$ we get$$ \cosh x \cosh 2x \cdots \cosh nx =...
View ArticleAnswer by S4M for Compute $\lim_{x\to0} \frac{\cosh x\cosh 2x\cosh 3x \cdots...
You want to calculate $\displaystyle\lim_{x\rightarrow 0}\frac{\displaystyle\prod_{k=1}^n\cosh kx - 1}{x^2}$. Let's start by noticing that $\displaystyle\prod_{k=1}^n\cosh kx - 1 =...
View ArticleAnswer by Norbert for Compute $\lim_{x\to0} \frac{\cosh x\cosh 2x\cosh 3x...
Note that$$\cosh \alpha=1+\frac{\alpha^2}{2}+o(\alpha^2)$$for $\alpha\to0$. So for $x\to 0$ we have$$\prod\limits_{k=1}^n \cosh kx= \prod\limits_{k=1}^n \left(1+\frac{k^2 x^2}{2}+o(k^2...
View ArticleCompute $\lim_{x\to0} \frac{\cosh x\cosh 2x\cosh 3x \cdots \cosh nx-1}{x^2}$
Compute:$$\lim_{x\to0} \frac{\cosh x\cosh 2x\cosh 3x \cdots \cosh nx-1}{x^2}$$How would you tackle this problem? Thanks.
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