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Exponential and Trigonometric Derivatives : Path of a Particle

Find the length of the path x(t) = e^t, y(t) = e^t cos t, z(t) = e^t sint, from 0 to 2.
A particle moves along the path x = e^2 t, y = 2e^t, z = t. What distance is traveled between times t = 0 and t = 1?

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The path of a particle is examined using derivatives. The solution is detailed and well presented.

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