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\[\large \int_0^\frac{\pi}{4}\sqrt{\tan x}\, dx\]

Find the value of the closed form of the above integral to 2 decimal places.

You may use a calculator for ...

The bitwise OR of two integers is the integer obtained by doing OR on each bit and concatenating them. Here is an example:

Chris has a list of ...

A massive particle is launched from ground level with a velocity of magnitude \(v\) and a launch angle of \(\theta\) with respect to the ground.

Suppose a large (essentially infinite ...

How many differentiable functions \( f: \mathbb{R} \rightarrow \mathbb{R} \) are there such that \( f(0) = 0 \) and

\[ y \frac{dy}{dx} = 2xy ? \]

Note: It is intentional that \(y\) appears ...

\[\large \lim_{m \to \infty} \lim_{n \to \infty} {(1 + \cos^{2m}(n! \pi x))} \]

Find the limit above, if \(x\) is irrational.

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