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\[\Large{g_{n} (x) = {x^{x^{{\cdots \text{n times} \cdots}^x}}}}\\ \\ \Large{h_n (x) = \displaystyle \sum_{r=0}^{n} \dfrac{x^r}{r!}}\]

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Find the area enclosed by the graph \(y = \lfloor x \rfloor\) and the \(x\)-axis \(\forall x \in \left(1,4\right)\).

If the answer is \(\alpha\) submit the value ...

\[\large \lim_{n\to \infty} \sum_{r=1}^{n^2} \frac 1r \sin \left(\frac{2017 r^2}{n^2}\right) \]

If the value of the limit above is ...

Joseph decided to play a game with 999 different players.

Setup:- There are 999 buckets kept in a row. Apart from these, the are two boxes, box-1 containing 999 red ...

Notes:

The corner of a square must lie on a grid dot.

All dots are equally ...

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