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\[\large \lim_{x \to \pi / 2} \frac {\left(1-\tan \frac x2\right)(1-\sin x)}{\left(1+\tan \frac x2\right)(\pi - 2x)^3} = \ ?\]

Let \(y\) be an implicit function of \(x\) defined by \(x^{2x} - 2x^x \cot y - 1 = 0\). Find \(y'(1)\).

We have a \(40W\) bulb and a \(60W\) bulb, both rated for \(120V\) AC supply. If we put these two together in series with a \(120V\) supply, how much power ...

Find the last digit of the sum: \(1^2 + 2^2 + 3^2 + \cdots + 2017^2\)

Let \(f(n)\) be the maximum number of pieces of pizza you can make by \(n\) straight cuts.

Find \(f(1) + f(2) + f(3) + \cdots + f(100)\).

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