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Under the influence of an electrical field that's caused by a dipole made of two opposite charges \(q_+=1~\mbox{C}\) and \(q_-=-1~\mbox{C}\) that are fixed ...

Find: \( \lim\limits_{k\to \infty}\lim\limits_{n\to \infty}\large \frac{\large \binom{nk}{n}^\frac{1}{n} }{k}\)

\[\large\lim _{ x\rightarrow 0 }{ \frac { ex }{ e-{ (1+x) }^{ 1/x } } }=? \]

\[ \large \lim_{x \to 0} \frac {(1-\cos x)(\sin x-x)(e^{x}+e^{-x}-2)}{x^{n}} \]

Find the minimum integer of \(n\) such that the limit above is ...

In the hexagonal circuit, each wire has resistance 1 ohm.

Find the equivalent resistance between points \(A\) and \(B\).

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